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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ lg(\frac{(3 - x)}{(a + x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg(\frac{-x}{(a + x)} + \frac{3}{(a + x)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(\frac{-x}{(a + x)} + \frac{3}{(a + x)})\right)}{dx}\\=&\frac{(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{ln{10}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})}\\=&\frac{x}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})(a + x)ln{10}} - \frac{3}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{x}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})(a + x)ln{10}} - \frac{3}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}}\right)}{dx}\\=&\frac{(\frac{-2(0 + 1)}{(a + x)^{3}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})x}{(a + x)^{2}ln{10}} + \frac{1}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{x*-0}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} - \frac{(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)ln{10}} - \frac{(\frac{-(0 + 1)}{(a + x)^{2}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})(a + x)ln^{2}{10}} - \frac{3(\frac{-2(0 + 1)}{(a + x)^{3}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{3(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{2}ln{10}} - \frac{3*-0}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}}\\=&\frac{-2x}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{x^{2}}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{x}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{2}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} - \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{2}ln{10}} - \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} + \frac{6}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{3x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{3}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{9}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2x}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{x^{2}}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{x}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{2}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} - \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{2}ln{10}} - \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} + \frac{6}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{3x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{3}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{9}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}}\right)}{dx}\\=&\frac{-2(\frac{-3(0 + 1)}{(a + x)^{4}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{2(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})x}{(a + x)^{3}ln{10}} - \frac{2}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{2x*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} - \frac{(\frac{-4(0 + 1)}{(a + x)^{5}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x^{2}}{(a + x)^{4}ln{10}} - \frac{2x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{x^{2}*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{(\frac{-3(0 + 1)}{(a + x)^{4}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{3}ln{10}} + \frac{1}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{x*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{3(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{4}ln{10}} + \frac{3}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3x*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{2(\frac{-2(0 + 1)}{(a + x)^{3}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{2(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{2}ln{10}} + \frac{2*-0}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{3}ln{10}} + \frac{(\frac{-3(0 + 1)}{(a + x)^{4}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} + \frac{x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln^{2}{10}} - \frac{(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{2}ln{10}} - \frac{(\frac{-2(0 + 1)}{(a + x)^{3}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{2}ln^{2}{10}} - \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{3}ln{10}} - \frac{3(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{3*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln^{2}{10}} + \frac{6(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{3}ln{10}} + \frac{6*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{4}ln{10}} + \frac{3(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} + \frac{3x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln^{2}{10}} - \frac{3(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{3}ln{10}} - \frac{3*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{9(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{4}ln{10}} - \frac{9(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{9*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln^{2}{10}}\\=&\frac{6x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6x^{2}}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{5x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{24x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{2x^{3}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{4x^{2}}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{7x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} + \frac{2x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{3}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{2x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{4x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} + \frac{18x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} - \frac{2}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{3}ln{10}} - \frac{12}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} - \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} - \frac{18}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{12x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{6}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{54}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6x^{2}}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{5x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{24x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{2x^{3}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{4x^{2}}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{7x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} + \frac{2x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{3}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{2x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{4x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} + \frac{18x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} - \frac{2}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{3}ln{10}} - \frac{12}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} - \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} - \frac{18}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{12x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{6}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{54}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}}\right)}{dx}\\=&\frac{6(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})x}{(a + x)^{4}ln{10}} + \frac{6}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6x*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{6(\frac{-5(0 + 1)}{(a + x)^{6}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{6(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x^{2}}{(a + x)^{5}ln{10}} + \frac{6*2x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{6x^{2}*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{5(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{5(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{4}ln{10}} - \frac{5}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{5x*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{24(\frac{-5(0 + 1)}{(a + x)^{6}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{24(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{5}ln{10}} - \frac{24}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{24x*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{6(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{6(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{3}ln{10}} - \frac{6*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{2(\frac{-6(0 + 1)}{(a + x)^{7}})x^{3}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{2(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{3}}{(a + x)^{6}ln{10}} + \frac{2*3x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{2x^{3}*-0}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{4(\frac{-5(0 + 1)}{(a + x)^{6}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{4(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{2}}{(a + x)^{5}ln{10}} - \frac{4*2x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{4x^{2}*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{12(\frac{-6(0 + 1)}{(a + x)^{7}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{2}}{(a + x)^{6}ln{10}} - \frac{12*2x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12x^{2}*-0}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{7(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{4}ln{10}} - \frac{7(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{7}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{7x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln^{2}{10}} + \frac{2(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{2(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{4}ln{10}} + \frac{2}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{2x*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} + \frac{18(\frac{-5(0 + 1)}{(a + x)^{6}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{5}ln{10}} + \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18x*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} + \frac{3(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{3}ln{10}} + \frac{3*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{18(\frac{-6(0 + 1)}{(a + x)^{7}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{6}ln{10}} + \frac{18}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18x*-0}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} + \frac{18(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{4}ln{10}} + \frac{18*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{18(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{4}ln{10}} + \frac{18(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln^{2}{10}} - \frac{2(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{2}}{(a + x)^{5}ln{10}} - \frac{2(\frac{-5(0 + 1)}{(a + x)^{6}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{2*2x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} - \frac{2x^{2}*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln^{2}{10}} + \frac{4(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{4}ln{10}} + \frac{4(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{4}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} + \frac{4x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln^{2}{10}} + \frac{18(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{5}ln{10}} + \frac{18(\frac{-5(0 + 1)}{(a + x)^{6}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{18x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln^{2}{10}} + \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{3}ln{10}} + \frac{3(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln^{2}{10}} - \frac{2(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{3}ln{10}} - \frac{2(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{2*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{3}ln^{2}{10}} - \frac{12(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{4}ln{10}} - \frac{12(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln^{2}{10}} - \frac{36(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{5}ln{10}} - \frac{36(\frac{-5(0 + 1)}{(a + x)^{6}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{36*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln^{2}{10}} - \frac{18(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{18(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{4}ln{10}} - \frac{18*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{18(\frac{-5(0 + 1)}{(a + x)^{6}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{5}ln{10}} + \frac{18*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{6(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{2}}{(a + x)^{6}ln{10}} - \frac{6(\frac{-6(0 + 1)}{(a + x)^{7}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{6*2x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{6x^{2}*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln^{2}{10}} + \frac{36(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{6}ln{10}} + \frac{36(\frac{-6(0 + 1)}{(a + x)^{7}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln^{2}{10}} - \frac{12(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{5}ln{10}} - \frac{12(\frac{-5(0 + 1)}{(a + x)^{6}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{12}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{12x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln^{2}{10}} - \frac{6(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{6(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{4}ln{10}} - \frac{6*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{18(\frac{-5(0 + 1)}{(a + x)^{6}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{18(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{5}ln{10}} - \frac{18*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{54(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{6}ln{10}} - \frac{54(\frac{-6(0 + 1)}{(a + x)^{7}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{54*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln^{2}{10}} + \frac{36(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{5}ln{10}} + \frac{36(\frac{-5(0 + 1)}{(a + x)^{6}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{36*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln^{2}{10}}\\=&\frac{-24x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{36x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{32x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{156x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{24}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{24x^{3}}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{42x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{156x^{2}}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{40x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{28x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{216x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{20}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{288x}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{132}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6x^{4}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} + \frac{12x^{3}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{7}ln{10}} + \frac{72x^{3}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} + \frac{30x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{12x^{3}}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{18x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{90x^{2}}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{44x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} - \frac{126x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{7}ln{10}} - \frac{324x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} - \frac{216x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{16}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} + \frac{6x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} + \frac{90x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} + \frac{8}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{216x}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} + \frac{96}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{432x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{7}ln{10}} + \frac{648x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} + \frac{252}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{120}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{396}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{84}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{18x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{6}ln{10}} + \frac{18x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{5}ln{10}} + \frac{126x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{6}ln{10}} + \frac{16}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} - \frac{6}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{4}ln{10}} - \frac{54}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{5}ln{10}} - \frac{216}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{6}ln{10}} - \frac{486}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{7}ln{10}} + \frac{72}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{144}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{108}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{60x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{7}ln{10}} - \frac{360x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{7}ln{10}} + \frac{60x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{6}ln{10}} - \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{108}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{162}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{486}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} + \frac{540}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{7}ln{10}} - \frac{180}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{6}ln{10}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ lg(\frac{(3 - x)}{(a + x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg(\frac{-x}{(a + x)} + \frac{3}{(a + x)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(\frac{-x}{(a + x)} + \frac{3}{(a + x)})\right)}{dx}\\=&\frac{(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{ln{10}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})}\\=&\frac{x}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})(a + x)ln{10}} - \frac{3}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{x}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})(a + x)ln{10}} - \frac{3}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}}\right)}{dx}\\=&\frac{(\frac{-2(0 + 1)}{(a + x)^{3}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})x}{(a + x)^{2}ln{10}} + \frac{1}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{x*-0}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} - \frac{(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)ln{10}} - \frac{(\frac{-(0 + 1)}{(a + x)^{2}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})(a + x)ln^{2}{10}} - \frac{3(\frac{-2(0 + 1)}{(a + x)^{3}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{3(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{2}ln{10}} - \frac{3*-0}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}}\\=&\frac{-2x}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{x^{2}}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{x}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{2}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} - \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{2}ln{10}} - \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} + \frac{6}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{3x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{3}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{9}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2x}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{x^{2}}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{x}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{2}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} - \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{2}ln{10}} - \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} + \frac{6}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{3x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{3}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{9}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}}\right)}{dx}\\=&\frac{-2(\frac{-3(0 + 1)}{(a + x)^{4}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{2(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})x}{(a + x)^{3}ln{10}} - \frac{2}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{2x*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} - \frac{(\frac{-4(0 + 1)}{(a + x)^{5}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x^{2}}{(a + x)^{4}ln{10}} - \frac{2x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{x^{2}*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{(\frac{-3(0 + 1)}{(a + x)^{4}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{3}ln{10}} + \frac{1}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{x*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{3(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{4}ln{10}} + \frac{3}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3x*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{2(\frac{-2(0 + 1)}{(a + x)^{3}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{2(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{2}ln{10}} + \frac{2*-0}{(a + x)^{2}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{3}ln{10}} + \frac{(\frac{-3(0 + 1)}{(a + x)^{4}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{1}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} + \frac{x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln^{2}{10}} - \frac{(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{2}ln{10}} - \frac{(\frac{-2(0 + 1)}{(a + x)^{3}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{2}ln^{2}{10}} - \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{3}ln{10}} - \frac{3(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{3*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln^{2}{10}} + \frac{6(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{3}ln{10}} + \frac{6*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{4}ln{10}} + \frac{3(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} + \frac{3x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln^{2}{10}} - \frac{3(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{3}ln{10}} - \frac{3*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{9(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{4}ln{10}} - \frac{9(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{9*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln^{2}{10}}\\=&\frac{6x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6x^{2}}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{5x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{24x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{2x^{3}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{4x^{2}}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{7x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} + \frac{2x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{3}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{2x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{4x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} + \frac{18x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} - \frac{2}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{3}ln{10}} - \frac{12}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} - \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} - \frac{18}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{12x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{6}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{54}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6x^{2}}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{5x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{24x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{2x^{3}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{4x^{2}}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{7x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} + \frac{2x}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{3}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{2x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{4x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} + \frac{18x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{3}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln{10}} - \frac{2}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{3}ln{10}} - \frac{12}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} - \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} - \frac{18}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{12x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{6}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{54}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}}\right)}{dx}\\=&\frac{6(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})x}{(a + x)^{4}ln{10}} + \frac{6}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} + \frac{6x*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{6(\frac{-5(0 + 1)}{(a + x)^{6}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{6(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x^{2}}{(a + x)^{5}ln{10}} + \frac{6*2x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{6x^{2}*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{5(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{5(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{4}ln{10}} - \frac{5}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{5x*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{24(\frac{-5(0 + 1)}{(a + x)^{6}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{24(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{5}ln{10}} - \frac{24}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{24x*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{6(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{6(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{3}ln{10}} - \frac{6*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{2(\frac{-6(0 + 1)}{(a + x)^{7}})x^{3}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{2(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{3}}{(a + x)^{6}ln{10}} + \frac{2*3x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{2x^{3}*-0}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{4(\frac{-5(0 + 1)}{(a + x)^{6}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{4(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{2}}{(a + x)^{5}ln{10}} - \frac{4*2x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{4x^{2}*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{12(\frac{-6(0 + 1)}{(a + x)^{7}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{2}}{(a + x)^{6}ln{10}} - \frac{12*2x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12x^{2}*-0}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{7(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{4}ln{10}} - \frac{7(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{7}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} - \frac{7x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln^{2}{10}} + \frac{2(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{2(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{4}ln{10}} + \frac{2}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{2x*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} + \frac{18(\frac{-5(0 + 1)}{(a + x)^{6}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{5}ln{10}} + \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18x*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} + \frac{3(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{3}ln{10}} + \frac{3*-0}{(a + x)^{3}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{18(\frac{-6(0 + 1)}{(a + x)^{7}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{6}ln{10}} + \frac{18}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18x*-0}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} + \frac{18(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{4}ln{10}} + \frac{18*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} + \frac{18(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{4}ln{10}} + \frac{18(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln^{2}{10}} - \frac{2(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{2}}{(a + x)^{5}ln{10}} - \frac{2(\frac{-5(0 + 1)}{(a + x)^{6}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{2*2x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} - \frac{2x^{2}*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln^{2}{10}} + \frac{4(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{4}ln{10}} + \frac{4(\frac{-4(0 + 1)}{(a + x)^{5}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{4}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} + \frac{4x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln^{2}{10}} + \frac{18(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{5}ln{10}} + \frac{18(\frac{-5(0 + 1)}{(a + x)^{6}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{18}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{18x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln^{2}{10}} + \frac{3(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{3}ln{10}} + \frac{3(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{3*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{3}ln^{2}{10}} - \frac{2(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{3}ln{10}} - \frac{2(\frac{-3(0 + 1)}{(a + x)^{4}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{2*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{3}ln^{2}{10}} - \frac{12(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{4}ln{10}} - \frac{12(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{12*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln^{2}{10}} - \frac{36(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{5}ln{10}} - \frac{36(\frac{-5(0 + 1)}{(a + x)^{6}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{36*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln^{2}{10}} - \frac{18(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{18(\frac{-(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}})}{(a + x)^{4}ln{10}} - \frac{18*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln^{2}{10}} + \frac{18(\frac{-5(0 + 1)}{(a + x)^{6}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{18(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{5}ln{10}} + \frac{18*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln^{2}{10}} - \frac{6(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x^{2}}{(a + x)^{6}ln{10}} - \frac{6(\frac{-6(0 + 1)}{(a + x)^{7}})x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{6*2x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{6x^{2}*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln^{2}{10}} + \frac{36(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})x}{(a + x)^{6}ln{10}} + \frac{36(\frac{-6(0 + 1)}{(a + x)^{7}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{36}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{36x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln^{2}{10}} - \frac{12(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})x}{(a + x)^{5}ln{10}} - \frac{12(\frac{-5(0 + 1)}{(a + x)^{6}})x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{12}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{12x*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln^{2}{10}} - \frac{6(\frac{-4(0 + 1)}{(a + x)^{5}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{6(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{4}ln{10}} - \frac{6*-0}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{18(\frac{-5(0 + 1)}{(a + x)^{6}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{18(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{5}ln{10}} - \frac{18*-0}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln^{2}{10}} - \frac{54(\frac{-3(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}})}{(a + x)^{6}ln{10}} - \frac{54(\frac{-6(0 + 1)}{(a + x)^{7}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{54*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln^{2}{10}} + \frac{36(\frac{-2(-(\frac{-(0 + 1)}{(a + x)^{2}})x - \frac{1}{(a + x)} + 3(\frac{-(0 + 1)}{(a + x)^{2}}))}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}})}{(a + x)^{5}ln{10}} + \frac{36(\frac{-5(0 + 1)}{(a + x)^{6}})}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{36*-0}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln^{2}{10}}\\=&\frac{-24x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{36x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{32x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{156x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{24}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{24x^{3}}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{42x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{156x^{2}}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{40x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{28x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{216x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{20}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{288x}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} - \frac{132}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} - \frac{6x^{4}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} + \frac{12x^{3}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{7}ln{10}} + \frac{72x^{3}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} + \frac{30x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} + \frac{12x^{3}}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{18x^{2}}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{90x^{2}}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{44x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} - \frac{126x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{7}ln{10}} - \frac{324x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} - \frac{216x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{16}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{4}ln{10}} + \frac{6x}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} + \frac{90x}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} + \frac{8}{(a + x)^{4}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{216x}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} + \frac{96}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{432x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{7}ln{10}} + \frac{648x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} + \frac{252}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{120}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{5}ln{10}} + \frac{396}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{6}ln{10}} - \frac{84}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{5}ln{10}} - \frac{18x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{6}ln{10}} + \frac{18x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{5}ln{10}} + \frac{126x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{6}ln{10}} + \frac{16}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{4}ln{10}} - \frac{6}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{4}ln{10}} - \frac{54}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{5}ln{10}} - \frac{216}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{6}ln{10}} - \frac{486}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{7}ln{10}} + \frac{72}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})ln{10}} - \frac{144}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}ln{10}} + \frac{108}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}ln{10}} + \frac{60x^{2}}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{7}ln{10}} - \frac{360x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{7}ln{10}} + \frac{60x}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{6}ln{10}} - \frac{18}{(a + x)^{5}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{108}{(a + x)^{6}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{162}{(a + x)^{7}(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}ln{10}} - \frac{486}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{4}(a + x)^{8}ln{10}} + \frac{540}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{3}(a + x)^{7}ln{10}} - \frac{180}{(\frac{-x}{(a + x)} + \frac{3}{(a + x)})^{2}(a + x)^{6}ln{10}}\\ \end{split}\end{equation} \]