Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ln({(xx + 3x + 3)}^{\frac{1}{2}} - {(xx + 3)}^{\frac{1}{2}})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})\right)}{dx}\\=&\frac{((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\=&\frac{x}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} + \frac{3}{2(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{x}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} + \frac{3}{2(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{1}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{2(x^{2} + 3x + 3)^{\frac{1}{2}}}\\=&\frac{-x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{1}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} - \frac{9}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{9}{4(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{1}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} - \frac{9}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{9}{4(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\right)}{dx}\\=&\frac{-(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{3}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3x + 3)} - \frac{(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{2*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{2}}{(x^{2} + 3)^{\frac{3}{2}}} + \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)} - \frac{3(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{(x^{2} + 3)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})}{4(x^{2} + 3x + 3)} - \frac{9(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{9(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{4(x^{2} + 3x + 3)^{\frac{3}{2}}}\\=&\frac{3x^{3}}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{27x^{2}}{2(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81x}{4(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{81x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2x}{(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{4x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{4x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{2}} + \frac{4x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{5}{2}}} + \frac{2x}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{27x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{9x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{27x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} - \frac{2x}{(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}} + \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{9}{2(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{81}{8(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3x^{3}}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{27x^{2}}{2(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81x}{4(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{81x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2x}{(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{4x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{4x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{2}} + \frac{4x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{5}{2}}} + \frac{2x}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{27x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{9x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{27x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} - \frac{2x}{(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}} + \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{9}{2(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{81}{8(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\right)}{dx}\\=&\frac{3(\frac{\frac{-5}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{7}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{3}}{(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{3*3x^{2}}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{27(\frac{\frac{-5}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{7}{2}}})x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{27(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{2}}{2(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{27*2x}{2(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3x + 3)^{2}} + \frac{3(\frac{-2(2x + 3 + 0)}{(x^{2} + 3x + 3)^{3}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{3*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{27(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{2(x^{2} + 3x + 3)^{2}} + \frac{27(\frac{-2(2x + 3 + 0)}{(x^{2} + 3x + 3)^{3}})x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{27*2x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{3*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{2}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81(\frac{\frac{-5}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{7}{2}}})x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{4(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{81}{4(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{81(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{4(x^{2} + 3x + 3)^{2}} + \frac{81(\frac{-2(2x + 3 + 0)}{(x^{2} + 3x + 3)^{3}})x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{81}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{9(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{9(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{9(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{9*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{3}}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{3}}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{2*3x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{2(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{2*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{9(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{9(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{9*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{2(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)} - \frac{2}{(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{4(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{4(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{4(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{4*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{12(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{12*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{4(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{4(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{4(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} + \frac{4*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3)^{2}} + \frac{3(\frac{-2(2x + 0)}{(x^{2} + 3)^{3}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{3*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{2}} + \frac{4(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x}{(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{4(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{4(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{4}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{3*2x}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{2(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{3*2x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{3}}{(x^{2} + 3)^{\frac{5}{2}}} - \frac{3(\frac{\frac{-5}{2}(2x + 0)}{(x^{2} + 3)^{\frac{7}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{5}{2}}} + \frac{2(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3)^{\frac{3}{2}}} + \frac{2}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{2(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} + \frac{2(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{2*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{27(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x}{2(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{27(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{27}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{6(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{6(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{6(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{6*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{9(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{9(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{9(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{9}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{6(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{6(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} + \frac{6*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{27(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{4(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{27(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{27(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{27}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} + \frac{3(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3)} - \frac{2}{(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{2}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3)^{\frac{3}{2}}} - \frac{2(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{2*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}} + \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3)^{\frac{3}{2}}} + \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{1}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x}{2(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{9(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{9(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)} - \frac{(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{9(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})}{2(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{9(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{9(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{27(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})}{4(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{27(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{9(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})}{2(x^{2} + 3x + 3)} - \frac{9(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{9(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{2(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})}{8(x^{2} + 3x + 3)^{2}} + \frac{81(\frac{-2(2x + 3 + 0)}{(x^{2} + 3x + 3)^{3}})}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{81(\frac{\frac{-5}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{7}{2}}})}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{8(x^{2} + 3x + 3)^{\frac{5}{2}}}\\=&\frac{-15x^{4}}{(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{90x^{3}}{(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{15x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} - \frac{90x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} + \frac{12x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{5}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{9x^{2}}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{405x^{2}}{2(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{5x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{405x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} + \frac{54x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{5}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{5}{2}}} - \frac{12x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} - \frac{72x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{2}} + \frac{13x^{2}}{(x^{2} + 3x + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{3}{2}}} + \frac{27x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{2}} - \frac{8x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{33x}{(x^{2} + 3x + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{81x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{162x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{3x^{4}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{13x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{3x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{5}{2}}} - \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{81x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{5}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27x}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{7x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{405x}{2(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} - \frac{10x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{2x^{4}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{9x^{4}}{(x^{2} + 3)^{\frac{5}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{24x}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{36x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{2}} - \frac{18x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{10x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} + \frac{18x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{3}{2}}} + \frac{81x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{2}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)} + \frac{9x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{6x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}} - \frac{81x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} - \frac{4x^{4}}{(x^{2} + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{6x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{243x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{6x^{3}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{15x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{3}} + \frac{18x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{27x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{5x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{2}} - \frac{6x^{2}}{(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)(x^{2} + 3x + 3)} + \frac{2x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)} - \frac{12x^{2}}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{8x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{18x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)} + \frac{81x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)(x^{2} + 3)} + \frac{12x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{5}{2}}} + \frac{4x^{4}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{24x}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{54x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)(x^{2} + 3x + 3)} + \frac{12x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{8x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} - \frac{6x^{3}}{(x^{2} + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{12x^{2}}{(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{243x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{54x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)(x^{2} + 3)} + \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}} + \frac{13x^{2}}{(x^{2} + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{9x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{2}} - \frac{15x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{6x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27x^{3}}{2(x^{2} + 3)^{\frac{5}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{21x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{162x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{3}{2}}} + \frac{81x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{6x}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{4x^{4}}{(x^{2} + 3)^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{9x^{3}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{5}{2}}} - \frac{15x^{2}}{(x^{2} + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{9x^{2}}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{12x}{(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{21x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{15x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{7}{2}}} + \frac{6x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)} + \frac{12x}{(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{9x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{81x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{2}} + \frac{243x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{81x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)(x^{2} + 3x + 3)} + \frac{6x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{243x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{81x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)(x^{2} + 3)} + \frac{27x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)} - \frac{6x^{3}}{(x^{2} + 3)^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{27x^{2}}{4(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{9x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)} - \frac{6x^{2}}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{2x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{81x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{5}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} - \frac{15x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{9x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{9x}{2(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{9x^{2}}{2(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{15x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{5}{2}}} - \frac{405x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} + \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{18x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{2}} - \frac{27}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{4}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{45}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2}{(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2}{(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{1}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{2}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} + \frac{2}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{81}{2(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{243}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} + \frac{27}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{1215}{16((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} - \frac{243}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} - \frac{1215}{16(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ln({(xx + 3x + 3)}^{\frac{1}{2}} - {(xx + 3)}^{\frac{1}{2}})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})\right)}{dx}\\=&\frac{((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\=&\frac{x}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} + \frac{3}{2(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{x}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} + \frac{3}{2(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{1}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{2(x^{2} + 3x + 3)^{\frac{1}{2}}}\\=&\frac{-x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{1}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} - \frac{9}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{9}{4(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{1}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{1}{2}}} - \frac{9}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{9}{4(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\right)}{dx}\\=&\frac{-(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{3}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3x + 3)} - \frac{(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{2*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{2}}{(x^{2} + 3)^{\frac{3}{2}}} + \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)} - \frac{3(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} + \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{(x^{2} + 3)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})}{4(x^{2} + 3x + 3)} - \frac{9(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{9(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{4(x^{2} + 3x + 3)^{\frac{3}{2}}}\\=&\frac{3x^{3}}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{27x^{2}}{2(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81x}{4(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{81x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2x}{(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{4x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{4x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{2}} + \frac{4x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{5}{2}}} + \frac{2x}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{27x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{9x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{27x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} - \frac{2x}{(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}} + \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{9}{2(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{81}{8(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3x^{3}}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{27x^{2}}{2(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81x}{4(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{81x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2x}{(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{4x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{4x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{2}} + \frac{4x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{5}{2}}} + \frac{2x}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{27x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{9x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{27x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} - \frac{2x}{(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}} + \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{9}{2(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{81}{8(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\right)}{dx}\\=&\frac{3(\frac{\frac{-5}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{7}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{3}}{(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{3*3x^{2}}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{27(\frac{\frac{-5}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{7}{2}}})x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{27(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{2}}{2(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{27*2x}{2(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3x + 3)^{2}} + \frac{3(\frac{-2(2x + 3 + 0)}{(x^{2} + 3x + 3)^{3}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{3*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{27(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{2(x^{2} + 3x + 3)^{2}} + \frac{27(\frac{-2(2x + 3 + 0)}{(x^{2} + 3x + 3)^{3}})x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{27*2x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{3*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{2}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81(\frac{\frac{-5}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{7}{2}}})x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{4(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{81}{4(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{81(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{4(x^{2} + 3x + 3)^{2}} + \frac{81(\frac{-2(2x + 3 + 0)}{(x^{2} + 3x + 3)^{3}})x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{81}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{9(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{9(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{9(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{9*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{3}}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{3}}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{2*3x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{2(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{2*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{9(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{9(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{9*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{2(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)} - \frac{2}{(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{4(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{4(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{4(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{4*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{12(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{12*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{4(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{4(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{4(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} + \frac{4*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{3}}{(x^{2} + 3)^{2}} + \frac{3(\frac{-2(2x + 0)}{(x^{2} + 3)^{3}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{3*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{2}} + \frac{4(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x}{(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{4(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{4(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{4}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{3*2x}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{3(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x^{2}}{2(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{3*2x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x^{3}}{(x^{2} + 3)^{\frac{5}{2}}} - \frac{3(\frac{\frac{-5}{2}(2x + 0)}{(x^{2} + 3)^{\frac{7}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{3*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{5}{2}}} + \frac{2(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3)^{\frac{3}{2}}} + \frac{2}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{2(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{2(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} + \frac{2(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{2*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{27(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x}{2(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{27(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{27}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{6(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{6(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{6(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{6*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{9(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{9(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{9(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{9}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{6(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{6(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} + \frac{6*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{27(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{4(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{27(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{27(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{27}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{3(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{3(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} + \frac{3(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{3*2x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3)} - \frac{2}{(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{2}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{2(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x^{3}}{(x^{2} + 3)^{\frac{3}{2}}} - \frac{2(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{2*3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}} + \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3)^{\frac{3}{2}}} + \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})x}{(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{1}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})x}{2(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{9(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)} - \frac{9(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}} - \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3x + 3)} - \frac{(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})x}{(x^{2} + 3)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 3)^{2}})x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} + \frac{9(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})}{2(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{9(\frac{\frac{-1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{3}{2}}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{9(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{3}{2}}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{27(\frac{-3((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}})}{4(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{27(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{9(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})}{2(x^{2} + 3x + 3)} - \frac{9(\frac{-(2x + 3 + 0)}{(x^{2} + 3x + 3)^{2}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{9(\frac{\frac{-3}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{5}{2}}})}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{9(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{2(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81(\frac{-2((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}})}{8(x^{2} + 3x + 3)^{2}} + \frac{81(\frac{-2(2x + 3 + 0)}{(x^{2} + 3x + 3)^{3}})}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{81(\frac{\frac{-5}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{7}{2}}})}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81(\frac{-((\frac{\frac{1}{2}(2x + 3 + 0)}{(x^{2} + 3x + 3)^{\frac{1}{2}}}) - (\frac{\frac{1}{2}(2x + 0)}{(x^{2} + 3)^{\frac{1}{2}}}))}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}})}{8(x^{2} + 3x + 3)^{\frac{5}{2}}}\\=&\frac{-15x^{4}}{(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{90x^{3}}{(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{15x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} - \frac{90x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} + \frac{12x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{5}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{9x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{9x^{2}}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{405x^{2}}{2(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{5x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{405x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} + \frac{54x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{5}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{5}{2}}} - \frac{12x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} - \frac{72x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{2}} + \frac{13x^{2}}{(x^{2} + 3x + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{3}{2}}} + \frac{27x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{2}} - \frac{8x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} + \frac{33x}{(x^{2} + 3x + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{81x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{162x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{3x^{4}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{13x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{3x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{5}{2}}} - \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{81x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{5}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27x}{(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{7x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{405x}{2(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} - \frac{10x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{2x^{4}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{9x^{4}}{(x^{2} + 3)^{\frac{5}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{24x}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{36x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{2}} - \frac{18x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{10x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} + \frac{18x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{3}{2}}} + \frac{81x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{2}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)} + \frac{9x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{6x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}} - \frac{81x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} - \frac{4x^{4}}{(x^{2} + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{6x^{2}}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{243x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{2}(x^{2} + 3)^{\frac{1}{2}}} + \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{6x^{3}}{(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{15x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{3}} + \frac{18x}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{27x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{3x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}} + \frac{5x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{2}} - \frac{6x^{2}}{(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)(x^{2} + 3x + 3)} + \frac{2x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)} - \frac{12x^{2}}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{8x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{18x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)} + \frac{81x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)(x^{2} + 3)} + \frac{12x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{5}{2}}} + \frac{4x^{4}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{24x}{(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{54x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)(x^{2} + 3x + 3)} + \frac{12x^{3}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{8x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)} - \frac{6x^{3}}{(x^{2} + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{12x^{2}}{(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{243x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{54x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)(x^{2} + 3)} + \frac{18x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{6x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}} + \frac{13x^{2}}{(x^{2} + 3)^{2}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{9x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{2}} - \frac{15x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{6x^{2}}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{27x^{3}}{2(x^{2} + 3)^{\frac{5}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{21x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{162x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} + \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{3}{2}}} + \frac{81x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{6x}{(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{4x^{4}}{(x^{2} + 3)^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{9x^{3}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{5}{2}}} - \frac{15x^{2}}{(x^{2} + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{9x^{2}}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{12x}{(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{21x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} - \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} + \frac{15x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{7}{2}}} + \frac{6x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)} + \frac{12x}{(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{9x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{81x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} - \frac{6x^{4}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{2}} + \frac{243x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{81x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)(x^{2} + 3x + 3)} + \frac{6x}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{243x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{2}(x^{2} + 3)^{\frac{1}{2}}} - \frac{81x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)(x^{2} + 3)} + \frac{27x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{27x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)} - \frac{6x^{3}}{(x^{2} + 3)^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} + \frac{27x^{2}}{4(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{9x^{2}}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)} - \frac{6x^{2}}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}} - \frac{2x^{2}}{(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{81x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{5}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{2x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} - \frac{15x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{12x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{9x^{3}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{3x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{3}{2}}} - \frac{9x}{2(x^{2} + 3)^{\frac{3}{2}}(x^{2} + 3x + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{9x^{2}}{2(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{15x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)(x^{2} + 3x + 3)^{\frac{1}{2}}} - \frac{3x^{2}}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{5}{2}}} - \frac{405x}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} + \frac{3x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)} + \frac{18x}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{81x}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)^{2}} - \frac{27}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{3}{2}}(x^{2} + 3)^{\frac{1}{2}}} + \frac{4}{(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} + \frac{2}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{\frac{1}{2}}(x^{2} + 3)^{\frac{1}{2}}} - \frac{45}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)(x^{2} + 3)^{\frac{1}{2}}} - \frac{9}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3)^{\frac{1}{2}}(x^{2} + 3x + 3)} - \frac{2}{(x^{2} + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{2}{(x^{2} + 3x + 3)((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3)} - \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)} - \frac{1}{(x^{2} + 3x + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{2}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3x + 3)^{\frac{3}{2}}} + \frac{1}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})(x^{2} + 3)^{\frac{3}{2}}} + \frac{2}{(x^{2} + 3)^{\frac{3}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} + \frac{81}{2((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{2}} + \frac{81}{2(x^{2} + 3x + 3)^{\frac{5}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})} - \frac{243}{8((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{4}(x^{2} + 3x + 3)^{2}} + \frac{27}{((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{3}{2}}} - \frac{1215}{16((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{2}(x^{2} + 3x + 3)^{3}} - \frac{243}{4((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})^{3}(x^{2} + 3x + 3)^{\frac{5}{2}}} - \frac{1215}{16(x^{2} + 3x + 3)^{\frac{7}{2}}((x^{2} + 3x + 3)^{\frac{1}{2}} - (x^{2} + 3)^{\frac{1}{2}})}\\ \end{split}\end{equation} \]