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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (2 - x)lg(sqrt(4 - 4x + xx))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2lg(sqrt(x^{2} - 4x + 4)) - xlg(sqrt(x^{2} - 4x + 4))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2lg(sqrt(x^{2} - 4x + 4)) - xlg(sqrt(x^{2} - 4x + 4))\right)}{dx}\\=&\frac{2(2x - 4 + 0)*\frac{1}{2}}{ln{10}(sqrt(x^{2} - 4x + 4))(x^{2} - 4x + 4)^{\frac{1}{2}}} - lg(sqrt(x^{2} - 4x + 4)) - \frac{x(2x - 4 + 0)*\frac{1}{2}}{ln{10}(sqrt(x^{2} - 4x + 4))(x^{2} - 4x + 4)^{\frac{1}{2}}}\\=&\frac{4x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{4}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - lg(sqrt(x^{2} - 4x + 4)) - \frac{x^{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{4}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - lg(sqrt(x^{2} - 4x + 4)) - \frac{x^{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)}\right)}{dx}\\=&\frac{4(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{4}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{4x*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{4x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{4(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{4*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{4*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{(2x - 4 + 0)*\frac{1}{2}}{ln{10}(sqrt(x^{2} - 4x + 4))(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})x^{2}}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{2x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{x^{2}*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{x^{2}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}}\\=&\frac{-6x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{12x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{x^{3}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{6x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{12x}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{x^{3}}{(x^{2} - 4x + 4)^{2}ln{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{12x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{x^{3}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{6x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{12x}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{x^{3}}{(x^{2} - 4x + 4)^{2}ln{10}}\right)}{dx}\\=&\frac{-6(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x^{2}}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{6*2x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{6x^{2}*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{6x^{2}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{12(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{12}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{12x*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{12x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{6*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{3x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x^{3}}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{3x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{x^{3}*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{x^{3}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{8(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{8*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{8(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})}{ln{10}} - \frac{8*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} - \frac{6(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x^{2}}{ln{10}} - \frac{6*2x}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{6x^{2}*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} + \frac{12(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x}{ln{10}} + \frac{12}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{12x*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} + \frac{(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x^{3}}{ln{10}} + \frac{3x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{x^{3}*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}}\\=&\frac{24x^{3}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{72x^{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{24x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{96x}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x^{4}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{160x}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{24x}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{3}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{120x^{2}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{48}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{40x^{3}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{5x^{4}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{24}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{80}{(x^{2} - 4x + 4)^{3}ln{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{24x^{3}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{72x^{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{24x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{96x}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x^{4}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{160x}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{24x}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{3}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{120x^{2}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{48}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{40x^{3}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{5x^{4}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{24}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{80}{(x^{2} - 4x + 4)^{3}ln{10}}\right)}{dx}\\=&\frac{24(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})x^{3}}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24*3x^{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24x^{3}*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{24x^{3}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{72(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})x^{2}}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{72*2x}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{72x^{2}*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{72x^{2}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{24(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{24}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{24x*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{24x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{96(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{96}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{96x*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{96x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x^{2}}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6*2x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})x^{4}}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3*4x^{3}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x^{4}*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{3x^{4}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{24(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{24*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{160(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})x}{ln{10}} + \frac{160}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{160x*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}} - \frac{24(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x}{ln{10}} - \frac{24}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{24x*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} - \frac{3(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{3*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{120(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})x^{2}}{ln{10}} - \frac{120*2x}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{120x^{2}*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}} - \frac{48(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{48*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{48*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{6(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x^{2}}{ln{10}} + \frac{6*2x}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{6x^{2}*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} + \frac{40(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})x^{3}}{ln{10}} + \frac{40*3x^{2}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{40x^{3}*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}} - \frac{5(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})x^{4}}{ln{10}} - \frac{5*4x^{3}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{5x^{4}*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}} + \frac{24(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})}{ln{10}} + \frac{24*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} - \frac{80(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})}{ln{10}} - \frac{80*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}}\\=&\frac{-150x^{4}}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{600x^{3}}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{180x^{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{1200x^{2}}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{360x}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{1200x}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{30x^{3}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{15x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{30}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{15x^{5}}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{600x}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{330x^{4}}{(x^{2} - 4x + 4)^{4}ln{10}} + \frac{240}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{2640x}{(x^{2} - 4x + 4)^{4}ln{10}} + \frac{1320x^{3}}{(x^{2} - 4x + 4)^{4}ln{10}} - \frac{2640x^{2}}{(x^{2} - 4x + 4)^{4}ln{10}} - \frac{50x^{3}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{300x^{2}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{33x^{5}}{(x^{2} - 4x + 4)^{4}ln{10}} - \frac{480}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{30}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{15x}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{400}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{1056}{(x^{2} - 4x + 4)^{4}ln{10}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (2 - x)lg(sqrt(4 - 4x + xx))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2lg(sqrt(x^{2} - 4x + 4)) - xlg(sqrt(x^{2} - 4x + 4))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2lg(sqrt(x^{2} - 4x + 4)) - xlg(sqrt(x^{2} - 4x + 4))\right)}{dx}\\=&\frac{2(2x - 4 + 0)*\frac{1}{2}}{ln{10}(sqrt(x^{2} - 4x + 4))(x^{2} - 4x + 4)^{\frac{1}{2}}} - lg(sqrt(x^{2} - 4x + 4)) - \frac{x(2x - 4 + 0)*\frac{1}{2}}{ln{10}(sqrt(x^{2} - 4x + 4))(x^{2} - 4x + 4)^{\frac{1}{2}}}\\=&\frac{4x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{4}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - lg(sqrt(x^{2} - 4x + 4)) - \frac{x^{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{4}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - lg(sqrt(x^{2} - 4x + 4)) - \frac{x^{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)}\right)}{dx}\\=&\frac{4(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{4}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{4x*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{4x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{4(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{4*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{4*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{(2x - 4 + 0)*\frac{1}{2}}{ln{10}(sqrt(x^{2} - 4x + 4))(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})x^{2}}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{2x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{x^{2}*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{x^{2}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}}\\=&\frac{-6x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{12x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{x^{3}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{6x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{12x}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{x^{3}}{(x^{2} - 4x + 4)^{2}ln{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{12x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{x^{3}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{6x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{12x}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{x^{3}}{(x^{2} - 4x + 4)^{2}ln{10}}\right)}{dx}\\=&\frac{-6(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x^{2}}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{6*2x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{6x^{2}*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{6x^{2}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{12(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{12}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{12x*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{12x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{6*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{3x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x^{3}}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{3x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{x^{3}*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{x^{3}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{8(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{8*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{8*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{8(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})}{ln{10}} - \frac{8*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} - \frac{6(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x^{2}}{ln{10}} - \frac{6*2x}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{6x^{2}*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} + \frac{12(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x}{ln{10}} + \frac{12}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{12x*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} + \frac{(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x^{3}}{ln{10}} + \frac{3x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{x^{3}*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}}\\=&\frac{24x^{3}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{72x^{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{24x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{96x}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x^{4}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{160x}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{24x}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{3}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{120x^{2}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{48}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{40x^{3}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{5x^{4}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{24}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{80}{(x^{2} - 4x + 4)^{3}ln{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{24x^{3}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{72x^{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{24x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{96x}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x^{4}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{160x}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{24x}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{3}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{120x^{2}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{48}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{40x^{3}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{5x^{4}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{24}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{80}{(x^{2} - 4x + 4)^{3}ln{10}}\right)}{dx}\\=&\frac{24(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})x^{3}}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24*3x^{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24x^{3}*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{24x^{3}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{72(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})x^{2}}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{72*2x}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{72x^{2}*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{72x^{2}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{24(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{24}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{24x*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{24x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{96(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})x}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{96}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{96x*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{96x*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})x^{2}}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6*2x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{6x^{2}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})x^{4}}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3*4x^{3}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3x^{4}*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{3x^{4}*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{24(\frac{\frac{-3}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{5}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} + \frac{24*-0}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} + \frac{24*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{160(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})x}{ln{10}} + \frac{160}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{160x*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}} - \frac{24(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x}{ln{10}} - \frac{24}{(x^{2} - 4x + 4)^{2}ln{10}} - \frac{24x*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} - \frac{3(\frac{\frac{-1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{3}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{3*-0}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{3*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{120(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})x^{2}}{ln{10}} - \frac{120*2x}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{120x^{2}*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}} - \frac{48(\frac{\frac{-5}{2}(2x - 4 + 0)}{(x^{2} - 4x + 4)^{\frac{7}{2}}})}{ln{10}sqrt(x^{2} - 4x + 4)} - \frac{48*-0}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln^{2}{10}sqrt(x^{2} - 4x + 4)} - \frac{48*-(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}(x^{2} - 4x + 4)(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{6(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})x^{2}}{ln{10}} + \frac{6*2x}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{6x^{2}*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} + \frac{40(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})x^{3}}{ln{10}} + \frac{40*3x^{2}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{40x^{3}*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}} - \frac{5(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})x^{4}}{ln{10}} - \frac{5*4x^{3}}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{5x^{4}*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}} + \frac{24(\frac{-2(2x - 4 + 0)}{(x^{2} - 4x + 4)^{3}})}{ln{10}} + \frac{24*-0}{(x^{2} - 4x + 4)^{2}ln^{2}{10}} - \frac{80(\frac{-3(2x - 4 + 0)}{(x^{2} - 4x + 4)^{4}})}{ln{10}} - \frac{80*-0}{(x^{2} - 4x + 4)^{3}ln^{2}{10}}\\=&\frac{-150x^{4}}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{600x^{3}}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{180x^{2}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{1200x^{2}}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{360x}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{1200x}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{30x^{3}}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{15x}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{30}{(x^{2} - 4x + 4)^{\frac{3}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{15x^{5}}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{600x}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{330x^{4}}{(x^{2} - 4x + 4)^{4}ln{10}} + \frac{240}{(x^{2} - 4x + 4)^{\frac{5}{2}}ln{10}sqrt(x^{2} - 4x + 4)} + \frac{2640x}{(x^{2} - 4x + 4)^{4}ln{10}} + \frac{1320x^{3}}{(x^{2} - 4x + 4)^{4}ln{10}} - \frac{2640x^{2}}{(x^{2} - 4x + 4)^{4}ln{10}} - \frac{50x^{3}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{300x^{2}}{(x^{2} - 4x + 4)^{3}ln{10}} + \frac{33x^{5}}{(x^{2} - 4x + 4)^{4}ln{10}} - \frac{480}{(x^{2} - 4x + 4)^{\frac{7}{2}}ln{10}sqrt(x^{2} - 4x + 4)} - \frac{30}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{15x}{(x^{2} - 4x + 4)^{2}ln{10}} + \frac{400}{(x^{2} - 4x + 4)^{3}ln{10}} - \frac{1056}{(x^{2} - 4x + 4)^{4}ln{10}}\\ \end{split}\end{equation} \]