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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{xln(x)}^{xe^{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{xln(x)}^{xe^{x}}\right)}{dx}\\=&(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})\\=&\frac{1}{xln(xln(x))} + \frac{1}{ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}}{xln(x)ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}}{xln(xln(x))}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{xln(xln(x))} + \frac{1}{ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}}{xln(x)ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}}{xln(xln(x))}\right)}{dx}\\=&\frac{-1}{x^{2}ln(xln(x))} + \frac{-(ln(x) + \frac{x}{(x)})}{xln^{2}(xln(x))(xln(x))} + \frac{-(ln(x) + \frac{x}{(x)})}{ln^{2}(xln(x))(xln(x))} - \frac{-log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln(xln(x))} - \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{xln(x)ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}*-1}{xln^{2}(x)(x)ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{xln(x)ln^{2}(xln(x))(xln(x))} - \frac{-log_{xln(x)}^{xe^{x}}}{x^{2}ln(xln(x))} - \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{xln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{xln^{2}(xln(x))(xln(x))}\\=&\frac{-1}{x^{2}ln(x)ln^{2}(xln(x))} - \frac{1}{xln(x)ln^{2}(xln(x))} - \frac{1}{x^{2}ln^{2}(xln(x))ln(x)} - \frac{1}{xln^{2}(xln(x))ln(x)} - \frac{2}{x^{2}ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln(xln(x))} - \frac{1}{x^{2}ln(xln(x))} - \frac{2}{xln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(x)ln(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln(xln(x))}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{x^{2}ln(x)ln^{2}(xln(x))} - \frac{1}{xln(x)ln^{2}(xln(x))} - \frac{1}{x^{2}ln^{2}(xln(x))ln(x)} - \frac{1}{xln^{2}(xln(x))ln(x)} - \frac{2}{x^{2}ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln(xln(x))} - \frac{1}{x^{2}ln(xln(x))} - \frac{2}{xln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(x)ln(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln(xln(x))}\right)}{dx}\\=&\frac{--2}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{-1}{x^{2}ln^{2}(x)(x)ln^{2}(xln(x))} - \frac{-2(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{3}(xln(x))(xln(x))} - \frac{-1}{x^{2}ln(x)ln^{2}(xln(x))} - \frac{-1}{xln^{2}(x)(x)ln^{2}(xln(x))} - \frac{-2(ln(x) + \frac{x}{(x)})}{xln(x)ln^{3}(xln(x))(xln(x))} - \frac{-2}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))ln(x)} - \frac{-1}{x^{2}ln^{2}(xln(x))ln^{2}(x)(x)} - \frac{-1}{x^{2}ln^{2}(xln(x))ln(x)} - \frac{-2(ln(x) + \frac{x}{(x)})}{xln^{3}(xln(x))(xln(x))ln(x)} - \frac{-1}{xln^{2}(xln(x))ln^{2}(x)(x)} - \frac{2*-2}{x^{3}ln^{2}(xln(x))} - \frac{2*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))} + \frac{-2log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln(xln(x))} + \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln(x)ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-1}{x^{2}ln^{2}(x)(x)ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{2}(xln(x))(xln(x))} - \frac{-2}{x^{3}ln(xln(x))} - \frac{-(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(xln(x))(xln(x))} - \frac{2*-1}{x^{2}ln^{2}(xln(x))} - \frac{2*-2(ln(x) + \frac{x}{(x)})}{xln^{3}(xln(x))(xln(x))} + \frac{2*-2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln(x)} + \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))ln(x)} + \frac{2log_{xln(x)}^{xe^{x}}*-1}{x^{2}ln^{2}(xln(x))ln^{2}(x)(x)} + \frac{2*-2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-2}{x^{2}ln^{3}(x)(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(x)ln^{3}(xln(x))(xln(x))} + \frac{-2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln(xln(x))} + \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln^{2}(x)ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-2}{x^{2}ln^{3}(x)(x)ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(x)ln^{2}(xln(x))(xln(x))} + \frac{2*-2log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{2}(xln(x))} + \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-1}{x^{2}ln^{2}(x)(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{3}(xln(x))(xln(x))} + \frac{2*-2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))} + \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))} + \frac{-2log_{xln(x)}^{xe^{x}}}{x^{3}ln(xln(x))} + \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(xln(x))(xln(x))}\\=&\frac{3}{x^{3}ln(x)ln^{2}(xln(x))} + \frac{8}{x^{3}ln^{3}(xln(x))ln(x)} + \frac{8}{x^{2}ln^{3}(xln(x))ln(x)} + \frac{4}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{1}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{4}{x^{2}ln^{2}(x)ln^{3}(xln(x))} + \frac{3}{x^{3}ln^{2}(xln(x))ln(x)} + \frac{2}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{4}{x^{3}ln(x)ln^{3}(xln(x))} + \frac{2}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{4}{x^{2}ln(x)ln^{3}(xln(x))} + \frac{2}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{12log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))ln(x)} - \frac{10log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{2}{x^{2}ln^{3}(xln(x))ln^{2}(x)} + \frac{1}{x^{3}ln^{2}(xln(x))ln^{2}(x)} + \frac{1}{x^{2}ln^{2}(xln(x))ln^{2}(x)} + \frac{6}{x^{3}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln^{2}(x)} - \frac{12log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{6}{x^{3}ln^{3}(xln(x))} + \frac{2}{x^{3}ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln^{3}(xln(x))} - \frac{3log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln^{2}(xln(x))} + \frac{6}{x^{2}ln^{3}(xln(x))} + \frac{3}{x^{2}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{3}(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln(xln(x))}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3}{x^{3}ln(x)ln^{2}(xln(x))} + \frac{8}{x^{3}ln^{3}(xln(x))ln(x)} + \frac{8}{x^{2}ln^{3}(xln(x))ln(x)} + \frac{4}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{1}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{4}{x^{2}ln^{2}(x)ln^{3}(xln(x))} + \frac{3}{x^{3}ln^{2}(xln(x))ln(x)} + \frac{2}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{4}{x^{3}ln(x)ln^{3}(xln(x))} + \frac{2}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{4}{x^{2}ln(x)ln^{3}(xln(x))} + \frac{2}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{12log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))ln(x)} - \frac{10log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{2}{x^{2}ln^{3}(xln(x))ln^{2}(x)} + \frac{1}{x^{3}ln^{2}(xln(x))ln^{2}(x)} + \frac{1}{x^{2}ln^{2}(xln(x))ln^{2}(x)} + \frac{6}{x^{3}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln^{2}(x)} - \frac{12log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{6}{x^{3}ln^{3}(xln(x))} + \frac{2}{x^{3}ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln^{3}(xln(x))} - \frac{3log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln^{2}(xln(x))} + \frac{6}{x^{2}ln^{3}(xln(x))} + \frac{3}{x^{2}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{3}(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln(xln(x))}\right)}{dx}\\=&\frac{3*-3}{x^{4}ln(x)ln^{2}(xln(x))} + \frac{3*-1}{x^{3}ln^{2}(x)(x)ln^{2}(xln(x))} + \frac{3*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{3}(xln(x))(xln(x))} + \frac{8*-3}{x^{4}ln^{3}(xln(x))ln(x)} + \frac{8*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))ln(x)} + \frac{8*-1}{x^{3}ln^{3}(xln(x))ln^{2}(x)(x)} + \frac{8*-2}{x^{3}ln^{3}(xln(x))ln(x)} + \frac{8*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln^{4}(xln(x))(xln(x))ln(x)} + \frac{8*-1}{x^{2}ln^{3}(xln(x))ln^{2}(x)(x)} + \frac{4*-3}{x^{4}ln^{2}(x)ln^{3}(xln(x))} + \frac{4*-2}{x^{3}ln^{3}(x)(x)ln^{3}(xln(x))} + \frac{4*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{4}(xln(x))(xln(x))} + \frac{-2}{x^{3}ln(x)ln^{2}(xln(x))} + \frac{-1}{x^{2}ln^{2}(x)(x)ln^{2}(xln(x))} + \frac{-2(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{3}(xln(x))(xln(x))} + \frac{4*-2}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{4*-2}{x^{2}ln^{3}(x)(x)ln^{3}(xln(x))} + \frac{4*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(x)ln^{4}(xln(x))(xln(x))} + \frac{3*-3}{x^{4}ln^{2}(xln(x))ln(x)} + \frac{3*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))ln(x)} + \frac{3*-1}{x^{3}ln^{2}(xln(x))ln^{2}(x)(x)} + \frac{2*-2}{x^{3}ln^{2}(xln(x))ln(x)} + \frac{2*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))ln(x)} + \frac{2*-1}{x^{2}ln^{2}(xln(x))ln^{2}(x)(x)} + \frac{2*-2}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{2*-2}{x^{2}ln^{3}(x)(x)ln^{2}(xln(x))} + \frac{2*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(x)ln^{3}(xln(x))(xln(x))} + \frac{4*-3}{x^{4}ln(x)ln^{3}(xln(x))} + \frac{4*-1}{x^{3}ln^{2}(x)(x)ln^{3}(xln(x))} + \frac{4*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{4}(xln(x))(xln(x))} + \frac{2*-3}{x^{4}ln^{2}(x)ln^{2}(xln(x))} + \frac{2*-2}{x^{3}ln^{3}(x)(x)ln^{2}(xln(x))} + \frac{2*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{3}(xln(x))(xln(x))} + \frac{4*-2}{x^{3}ln(x)ln^{3}(xln(x))} + \frac{4*-1}{x^{2}ln^{2}(x)(x)ln^{3}(xln(x))} + \frac{4*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{4}(xln(x))(xln(x))} + \frac{2*-3}{x^{4}ln^{3}(xln(x))ln^{2}(x)} + \frac{2*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))ln^{2}(x)} + \frac{2*-2}{x^{3}ln^{3}(xln(x))ln^{3}(x)(x)} - \frac{2*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln(xln(x))} - \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln(x)ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{2}(x)(x)ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{2}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln(x)} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{6log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))ln(x)} - \frac{6log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{2}(xln(x))ln^{2}(x)(x)} - \frac{12*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln(x)} - \frac{12(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(xln(x))ln(x)} - \frac{12log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))ln(x)} - \frac{12log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{3}(xln(x))ln^{2}(x)(x)} - \frac{10*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{2}(xln(x))} - \frac{10(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(x)ln^{2}(xln(x))} - \frac{10log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{3}(x)(x)ln^{2}(xln(x))} - \frac{10log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{3}(xln(x))(xln(x))} + \frac{2*-2}{x^{3}ln^{3}(xln(x))ln^{2}(x)} + \frac{2*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln^{4}(xln(x))(xln(x))ln^{2}(x)} + \frac{2*-2}{x^{2}ln^{3}(xln(x))ln^{3}(x)(x)} + \frac{-3}{x^{4}ln^{2}(xln(x))ln^{2}(x)} + \frac{-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))ln^{2}(x)} + \frac{-2}{x^{3}ln^{2}(xln(x))ln^{3}(x)(x)} + \frac{-2}{x^{3}ln^{2}(xln(x))ln^{2}(x)} + \frac{-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))ln^{2}(x)} + \frac{-2}{x^{2}ln^{2}(xln(x))ln^{3}(x)(x)} + \frac{6*-3}{x^{4}ln^{2}(xln(x))} + \frac{6*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln^{2}(x)} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{6log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))ln^{2}(x)} - \frac{6log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{3}(xln(x))ln^{3}(x)(x)} - \frac{2*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln^{2}(x)} - \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{2}(xln(x))ln^{3}(x)(x)} - \frac{12*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{3}(xln(x))} - \frac{12(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(x)ln^{3}(xln(x))} - \frac{12log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{3}(x)(x)ln^{3}(xln(x))} - \frac{12log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{4}(xln(x))(xln(x))} + \frac{6*-3}{x^{4}ln^{3}(xln(x))} + \frac{6*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))} + \frac{2*-3}{x^{4}ln(xln(x))} + \frac{2*-(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{3}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(x)ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3}{x^{3}ln^{4}(x)(x)ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(x)ln^{4}(xln(x))(xln(x))} - \frac{3*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln(xln(x))} - \frac{3(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(x)ln(xln(x))} - \frac{3log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{3}(x)(x)ln(xln(x))} - \frac{3log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{2}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{2}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3}{x^{3}ln^{4}(x)(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(x)ln^{3}(xln(x))(xln(x))} + \frac{6*-2}{x^{3}ln^{3}(xln(x))} + \frac{6*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln^{4}(xln(x))(xln(x))} + \frac{3*-2}{x^{3}ln^{2}(xln(x))} + \frac{3*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{2}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{2}(x)(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{3}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{3}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln(x)ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{2}(x)(x)ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{4}(xln(x))(xln(x))} - \frac{2*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln(xln(x))} - \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(x)ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-3}{x^{3}ln^{4}(x)(x)ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(x)ln^{2}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))} - \frac{2*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln(xln(x))} - \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(xln(x))(xln(x))}\\=&\frac{-11}{x^{4}ln(x)ln^{2}(xln(x))} - \frac{48}{x^{4}ln^{3}(xln(x))ln(x)} - \frac{54}{x^{4}ln^{4}(xln(x))ln(x)} - \frac{36}{x^{4}ln^{2}(x)ln^{3}(xln(x))} - \frac{54}{x^{3}ln^{4}(xln(x))ln(x)} - \frac{36}{x^{4}ln^{2}(x)ln^{4}(xln(x))} - \frac{36}{x^{4}ln^{4}(xln(x))ln^{2}(x)} - \frac{34}{x^{3}ln^{3}(xln(x))ln(x)} - \frac{36}{x^{3}ln^{2}(x)ln^{4}(xln(x))} - \frac{36}{x^{3}ln^{4}(xln(x))ln^{2}(x)} - \frac{18}{x^{4}ln^{3}(x)ln^{4}(xln(x))} - \frac{2}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{22}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{26}{x^{3}ln^{2}(x)ln^{3}(xln(x))} - \frac{24}{x^{4}ln^{3}(xln(x))ln^{2}(x)} - \frac{18}{x^{3}ln^{3}(x)ln^{4}(xln(x))} - \frac{11}{x^{4}ln^{2}(xln(x))ln(x)} - \frac{6}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{7}{x^{3}ln^{2}(x)ln^{2}(xln(x))} - \frac{18}{x^{3}ln^{3}(x)ln^{3}(xln(x))} - \frac{24}{x^{4}ln(x)ln^{3}(xln(x))} - \frac{12}{x^{4}ln^{2}(x)ln^{2}(xln(x))} - \frac{18}{x^{4}ln^{3}(x)ln^{3}(xln(x))} - \frac{14}{x^{3}ln(x)ln^{3}(xln(x))} - \frac{6}{x^{4}ln^{2}(xln(x))ln^{2}(x)} - \frac{6}{x^{4}ln^{3}(x)ln^{2}(xln(x))} - \frac{5}{x^{3}ln^{2}(xln(x))ln^{2}(x)} - \frac{6}{x^{3}ln^{3}(x)ln^{2}(xln(x))} - \frac{18}{x^{4}ln(x)ln^{4}(xln(x))} + \frac{6log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln(xln(x))} + \frac{22log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln(x)} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln(x)} + \frac{46log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{2}(xln(x))} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(xln(x))ln(x)} + \frac{54log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln^{2}(x)} + \frac{90log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{3}(xln(x))} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(xln(x))ln^{2}(x)} + \frac{24log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(xln(x))ln^{3}(x)} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{4}(xln(x))} + \frac{12log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln^{2}(x)} + \frac{18log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln^{3}(x)} + \frac{90log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{3}(xln(x))} - \frac{18}{x^{3}ln(x)ln^{4}(xln(x))} - \frac{6}{x^{4}ln^{4}(xln(x))ln^{3}(x)} - \frac{6}{x^{3}ln^{4}(xln(x))ln^{3}(x)} - \frac{6}{x^{4}ln^{3}(xln(x))ln^{3}(x)} + \frac{4log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln^{3}(x)} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{4}(xln(x))} + \frac{24log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(x)ln^{4}(xln(x))} - \frac{6}{x^{3}ln^{3}(xln(x))ln^{3}(x)} - \frac{2}{x^{4}ln^{2}(xln(x))ln^{3}(x)} - \frac{2}{x^{3}ln^{2}(xln(x))ln^{3}(x)} - \frac{24}{x^{3}ln^{3}(xln(x))} + \frac{11log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln(xln(x))} + \frac{12log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln(xln(x))} + \frac{48log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{2}(xln(x))} + \frac{22log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(x)ln^{2}(xln(x))} + \frac{36log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(x)ln^{3}(xln(x))} + \frac{22log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{2}(xln(x))} - \frac{24}{x^{4}ln^{4}(xln(x))} - \frac{22}{x^{4}ln^{2}(xln(x))} + \frac{36log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{3}(xln(x))} + \frac{6log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(x)ln(xln(x))} - \frac{24}{x^{3}ln^{4}(xln(x))} - \frac{8}{x^{3}ln^{2}(xln(x))} + \frac{24log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{4}(xln(x))} + \frac{36log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))} - \frac{6}{x^{4}ln(xln(x))} - \frac{36}{x^{4}ln^{3}(xln(x))} + \frac{22log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))} + \frac{24log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(xln(x))} + \frac{6log_{xln(x)}^{xe^{x}}}{x^{4}ln(xln(x))}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{xln(x)}^{xe^{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{xln(x)}^{xe^{x}}\right)}{dx}\\=&(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})\\=&\frac{1}{xln(xln(x))} + \frac{1}{ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}}{xln(x)ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}}{xln(xln(x))}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{xln(xln(x))} + \frac{1}{ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}}{xln(x)ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}}{xln(xln(x))}\right)}{dx}\\=&\frac{-1}{x^{2}ln(xln(x))} + \frac{-(ln(x) + \frac{x}{(x)})}{xln^{2}(xln(x))(xln(x))} + \frac{-(ln(x) + \frac{x}{(x)})}{ln^{2}(xln(x))(xln(x))} - \frac{-log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln(xln(x))} - \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{xln(x)ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}*-1}{xln^{2}(x)(x)ln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{xln(x)ln^{2}(xln(x))(xln(x))} - \frac{-log_{xln(x)}^{xe^{x}}}{x^{2}ln(xln(x))} - \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{xln(xln(x))} - \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{xln^{2}(xln(x))(xln(x))}\\=&\frac{-1}{x^{2}ln(x)ln^{2}(xln(x))} - \frac{1}{xln(x)ln^{2}(xln(x))} - \frac{1}{x^{2}ln^{2}(xln(x))ln(x)} - \frac{1}{xln^{2}(xln(x))ln(x)} - \frac{2}{x^{2}ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln(xln(x))} - \frac{1}{x^{2}ln(xln(x))} - \frac{2}{xln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(x)ln(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln(xln(x))}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{x^{2}ln(x)ln^{2}(xln(x))} - \frac{1}{xln(x)ln^{2}(xln(x))} - \frac{1}{x^{2}ln^{2}(xln(x))ln(x)} - \frac{1}{xln^{2}(xln(x))ln(x)} - \frac{2}{x^{2}ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln(xln(x))} - \frac{1}{x^{2}ln(xln(x))} - \frac{2}{xln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(x)ln(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}}{x^{2}ln^{2}(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}}{x^{2}ln(xln(x))}\right)}{dx}\\=&\frac{--2}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{-1}{x^{2}ln^{2}(x)(x)ln^{2}(xln(x))} - \frac{-2(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{3}(xln(x))(xln(x))} - \frac{-1}{x^{2}ln(x)ln^{2}(xln(x))} - \frac{-1}{xln^{2}(x)(x)ln^{2}(xln(x))} - \frac{-2(ln(x) + \frac{x}{(x)})}{xln(x)ln^{3}(xln(x))(xln(x))} - \frac{-2}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))ln(x)} - \frac{-1}{x^{2}ln^{2}(xln(x))ln^{2}(x)(x)} - \frac{-1}{x^{2}ln^{2}(xln(x))ln(x)} - \frac{-2(ln(x) + \frac{x}{(x)})}{xln^{3}(xln(x))(xln(x))ln(x)} - \frac{-1}{xln^{2}(xln(x))ln^{2}(x)(x)} - \frac{2*-2}{x^{3}ln^{2}(xln(x))} - \frac{2*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))} + \frac{-2log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln(xln(x))} + \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln(x)ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-1}{x^{2}ln^{2}(x)(x)ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{2}(xln(x))(xln(x))} - \frac{-2}{x^{3}ln(xln(x))} - \frac{-(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(xln(x))(xln(x))} - \frac{2*-1}{x^{2}ln^{2}(xln(x))} - \frac{2*-2(ln(x) + \frac{x}{(x)})}{xln^{3}(xln(x))(xln(x))} + \frac{2*-2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln(x)} + \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))ln(x)} + \frac{2log_{xln(x)}^{xe^{x}}*-1}{x^{2}ln^{2}(xln(x))ln^{2}(x)(x)} + \frac{2*-2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-2}{x^{2}ln^{3}(x)(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(x)ln^{3}(xln(x))(xln(x))} + \frac{-2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln(xln(x))} + \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln^{2}(x)ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-2}{x^{2}ln^{3}(x)(x)ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(x)ln^{2}(xln(x))(xln(x))} + \frac{2*-2log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{2}(xln(x))} + \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-1}{x^{2}ln^{2}(x)(x)ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{3}(xln(x))(xln(x))} + \frac{2*-2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))} + \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln^{2}(xln(x))} + \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))} + \frac{-2log_{xln(x)}^{xe^{x}}}{x^{3}ln(xln(x))} + \frac{(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{2}ln(xln(x))} + \frac{log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(xln(x))(xln(x))}\\=&\frac{3}{x^{3}ln(x)ln^{2}(xln(x))} + \frac{8}{x^{3}ln^{3}(xln(x))ln(x)} + \frac{8}{x^{2}ln^{3}(xln(x))ln(x)} + \frac{4}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{1}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{4}{x^{2}ln^{2}(x)ln^{3}(xln(x))} + \frac{3}{x^{3}ln^{2}(xln(x))ln(x)} + \frac{2}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{4}{x^{3}ln(x)ln^{3}(xln(x))} + \frac{2}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{4}{x^{2}ln(x)ln^{3}(xln(x))} + \frac{2}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{12log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))ln(x)} - \frac{10log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{2}{x^{2}ln^{3}(xln(x))ln^{2}(x)} + \frac{1}{x^{3}ln^{2}(xln(x))ln^{2}(x)} + \frac{1}{x^{2}ln^{2}(xln(x))ln^{2}(x)} + \frac{6}{x^{3}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln^{2}(x)} - \frac{12log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{6}{x^{3}ln^{3}(xln(x))} + \frac{2}{x^{3}ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln^{3}(xln(x))} - \frac{3log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln^{2}(xln(x))} + \frac{6}{x^{2}ln^{3}(xln(x))} + \frac{3}{x^{2}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{3}(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln(xln(x))}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3}{x^{3}ln(x)ln^{2}(xln(x))} + \frac{8}{x^{3}ln^{3}(xln(x))ln(x)} + \frac{8}{x^{2}ln^{3}(xln(x))ln(x)} + \frac{4}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{1}{x^{2}ln(x)ln^{2}(xln(x))} + \frac{4}{x^{2}ln^{2}(x)ln^{3}(xln(x))} + \frac{3}{x^{3}ln^{2}(xln(x))ln(x)} + \frac{2}{x^{2}ln^{2}(xln(x))ln(x)} + \frac{2}{x^{2}ln^{2}(x)ln^{2}(xln(x))} + \frac{4}{x^{3}ln(x)ln^{3}(xln(x))} + \frac{2}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{4}{x^{2}ln(x)ln^{3}(xln(x))} + \frac{2}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{12log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))ln(x)} - \frac{10log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{2}{x^{2}ln^{3}(xln(x))ln^{2}(x)} + \frac{1}{x^{3}ln^{2}(xln(x))ln^{2}(x)} + \frac{1}{x^{2}ln^{2}(xln(x))ln^{2}(x)} + \frac{6}{x^{3}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))ln^{2}(x)} - \frac{12log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{6}{x^{3}ln^{3}(xln(x))} + \frac{2}{x^{3}ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln^{3}(xln(x))} - \frac{3log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln^{2}(xln(x))} + \frac{6}{x^{2}ln^{3}(xln(x))} + \frac{3}{x^{2}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln(x)ln^{3}(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(x)ln(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}}{x^{3}ln^{2}(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}}{x^{3}ln(xln(x))}\right)}{dx}\\=&\frac{3*-3}{x^{4}ln(x)ln^{2}(xln(x))} + \frac{3*-1}{x^{3}ln^{2}(x)(x)ln^{2}(xln(x))} + \frac{3*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{3}(xln(x))(xln(x))} + \frac{8*-3}{x^{4}ln^{3}(xln(x))ln(x)} + \frac{8*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))ln(x)} + \frac{8*-1}{x^{3}ln^{3}(xln(x))ln^{2}(x)(x)} + \frac{8*-2}{x^{3}ln^{3}(xln(x))ln(x)} + \frac{8*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln^{4}(xln(x))(xln(x))ln(x)} + \frac{8*-1}{x^{2}ln^{3}(xln(x))ln^{2}(x)(x)} + \frac{4*-3}{x^{4}ln^{2}(x)ln^{3}(xln(x))} + \frac{4*-2}{x^{3}ln^{3}(x)(x)ln^{3}(xln(x))} + \frac{4*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{4}(xln(x))(xln(x))} + \frac{-2}{x^{3}ln(x)ln^{2}(xln(x))} + \frac{-1}{x^{2}ln^{2}(x)(x)ln^{2}(xln(x))} + \frac{-2(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{3}(xln(x))(xln(x))} + \frac{4*-2}{x^{3}ln^{2}(x)ln^{3}(xln(x))} + \frac{4*-2}{x^{2}ln^{3}(x)(x)ln^{3}(xln(x))} + \frac{4*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(x)ln^{4}(xln(x))(xln(x))} + \frac{3*-3}{x^{4}ln^{2}(xln(x))ln(x)} + \frac{3*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))ln(x)} + \frac{3*-1}{x^{3}ln^{2}(xln(x))ln^{2}(x)(x)} + \frac{2*-2}{x^{3}ln^{2}(xln(x))ln(x)} + \frac{2*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))ln(x)} + \frac{2*-1}{x^{2}ln^{2}(xln(x))ln^{2}(x)(x)} + \frac{2*-2}{x^{3}ln^{2}(x)ln^{2}(xln(x))} + \frac{2*-2}{x^{2}ln^{3}(x)(x)ln^{2}(xln(x))} + \frac{2*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{2}(x)ln^{3}(xln(x))(xln(x))} + \frac{4*-3}{x^{4}ln(x)ln^{3}(xln(x))} + \frac{4*-1}{x^{3}ln^{2}(x)(x)ln^{3}(xln(x))} + \frac{4*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{4}(xln(x))(xln(x))} + \frac{2*-3}{x^{4}ln^{2}(x)ln^{2}(xln(x))} + \frac{2*-2}{x^{3}ln^{3}(x)(x)ln^{2}(xln(x))} + \frac{2*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{3}(xln(x))(xln(x))} + \frac{4*-2}{x^{3}ln(x)ln^{3}(xln(x))} + \frac{4*-1}{x^{2}ln^{2}(x)(x)ln^{3}(xln(x))} + \frac{4*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln(x)ln^{4}(xln(x))(xln(x))} + \frac{2*-3}{x^{4}ln^{3}(xln(x))ln^{2}(x)} + \frac{2*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))ln^{2}(x)} + \frac{2*-2}{x^{3}ln^{3}(xln(x))ln^{3}(x)(x)} - \frac{2*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln(xln(x))} - \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln(x)ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{2}(x)(x)ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{2}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln(x)} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{6log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))ln(x)} - \frac{6log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{2}(xln(x))ln^{2}(x)(x)} - \frac{12*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln(x)} - \frac{12(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(xln(x))ln(x)} - \frac{12log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))ln(x)} - \frac{12log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{3}(xln(x))ln^{2}(x)(x)} - \frac{10*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{2}(xln(x))} - \frac{10(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(x)ln^{2}(xln(x))} - \frac{10log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{3}(x)(x)ln^{2}(xln(x))} - \frac{10log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{3}(xln(x))(xln(x))} + \frac{2*-2}{x^{3}ln^{3}(xln(x))ln^{2}(x)} + \frac{2*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln^{4}(xln(x))(xln(x))ln^{2}(x)} + \frac{2*-2}{x^{2}ln^{3}(xln(x))ln^{3}(x)(x)} + \frac{-3}{x^{4}ln^{2}(xln(x))ln^{2}(x)} + \frac{-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))ln^{2}(x)} + \frac{-2}{x^{3}ln^{2}(xln(x))ln^{3}(x)(x)} + \frac{-2}{x^{3}ln^{2}(xln(x))ln^{2}(x)} + \frac{-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))ln^{2}(x)} + \frac{-2}{x^{2}ln^{2}(xln(x))ln^{3}(x)(x)} + \frac{6*-3}{x^{4}ln^{2}(xln(x))} + \frac{6*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln^{2}(x)} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{6log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))ln^{2}(x)} - \frac{6log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{3}(xln(x))ln^{3}(x)(x)} - \frac{2*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln^{2}(x)} - \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))ln^{2}(x)} - \frac{2log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{2}(xln(x))ln^{3}(x)(x)} - \frac{12*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{3}(xln(x))} - \frac{12(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(x)ln^{3}(xln(x))} - \frac{12log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{3}(x)(x)ln^{3}(xln(x))} - \frac{12log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{4}(xln(x))(xln(x))} + \frac{6*-3}{x^{4}ln^{3}(xln(x))} + \frac{6*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))} + \frac{2*-3}{x^{4}ln(xln(x))} + \frac{2*-(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{3}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(x)ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3}{x^{3}ln^{4}(x)(x)ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(x)ln^{4}(xln(x))(xln(x))} - \frac{3*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln(xln(x))} - \frac{3(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(x)ln(xln(x))} - \frac{3log_{xln(x)}^{xe^{x}}*-2}{x^{3}ln^{3}(x)(x)ln(xln(x))} - \frac{3log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(x)ln^{2}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{2}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3}{x^{3}ln^{4}(x)(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(x)ln^{3}(xln(x))(xln(x))} + \frac{6*-2}{x^{3}ln^{3}(xln(x))} + \frac{6*-3(ln(x) + \frac{x}{(x)})}{x^{2}ln^{4}(xln(x))(xln(x))} + \frac{3*-2}{x^{3}ln^{2}(xln(x))} + \frac{3*-2(ln(x) + \frac{x}{(x)})}{x^{2}ln^{3}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{2}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{2}(x)(x)ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{3}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{3}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln(x)ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-1}{x^{3}ln^{2}(x)(x)ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln(x)ln^{4}(xln(x))(xln(x))} - \frac{2*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln(xln(x))} - \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(x)ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-3}{x^{3}ln^{4}(x)(x)ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(x)ln^{2}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{3}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-3(ln(x) + \frac{x}{(x)})}{x^{3}ln^{4}(xln(x))(xln(x))} - \frac{6*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))} - \frac{6(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln^{2}(xln(x))} - \frac{6log_{xln(x)}^{xe^{x}}*-2(ln(x) + \frac{x}{(x)})}{x^{3}ln^{3}(xln(x))(xln(x))} - \frac{2*-3log_{xln(x)}^{xe^{x}}}{x^{4}ln(xln(x))} - \frac{2(\frac{(\frac{(e^{x} + xe^{x})}{(xe^{x})} - \frac{(ln(x) + \frac{x}{(x)})log_{xln(x)}^{xe^{x}}}{(xln(x))})}{(ln(xln(x)))})}{x^{3}ln(xln(x))} - \frac{2log_{xln(x)}^{xe^{x}}*-(ln(x) + \frac{x}{(x)})}{x^{3}ln^{2}(xln(x))(xln(x))}\\=&\frac{-11}{x^{4}ln(x)ln^{2}(xln(x))} - \frac{48}{x^{4}ln^{3}(xln(x))ln(x)} - \frac{54}{x^{4}ln^{4}(xln(x))ln(x)} - \frac{36}{x^{4}ln^{2}(x)ln^{3}(xln(x))} - \frac{54}{x^{3}ln^{4}(xln(x))ln(x)} - \frac{36}{x^{4}ln^{2}(x)ln^{4}(xln(x))} - \frac{36}{x^{4}ln^{4}(xln(x))ln^{2}(x)} - \frac{34}{x^{3}ln^{3}(xln(x))ln(x)} - \frac{36}{x^{3}ln^{2}(x)ln^{4}(xln(x))} - \frac{36}{x^{3}ln^{4}(xln(x))ln^{2}(x)} - \frac{18}{x^{4}ln^{3}(x)ln^{4}(xln(x))} - \frac{2}{x^{3}ln(x)ln^{2}(xln(x))} - \frac{22}{x^{3}ln^{3}(xln(x))ln^{2}(x)} - \frac{26}{x^{3}ln^{2}(x)ln^{3}(xln(x))} - \frac{24}{x^{4}ln^{3}(xln(x))ln^{2}(x)} - \frac{18}{x^{3}ln^{3}(x)ln^{4}(xln(x))} - \frac{11}{x^{4}ln^{2}(xln(x))ln(x)} - \frac{6}{x^{3}ln^{2}(xln(x))ln(x)} - \frac{7}{x^{3}ln^{2}(x)ln^{2}(xln(x))} - \frac{18}{x^{3}ln^{3}(x)ln^{3}(xln(x))} - \frac{24}{x^{4}ln(x)ln^{3}(xln(x))} - \frac{12}{x^{4}ln^{2}(x)ln^{2}(xln(x))} - \frac{18}{x^{4}ln^{3}(x)ln^{3}(xln(x))} - \frac{14}{x^{3}ln(x)ln^{3}(xln(x))} - \frac{6}{x^{4}ln^{2}(xln(x))ln^{2}(x)} - \frac{6}{x^{4}ln^{3}(x)ln^{2}(xln(x))} - \frac{5}{x^{3}ln^{2}(xln(x))ln^{2}(x)} - \frac{6}{x^{3}ln^{3}(x)ln^{2}(xln(x))} - \frac{18}{x^{4}ln(x)ln^{4}(xln(x))} + \frac{6log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln(xln(x))} + \frac{22log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln(x)} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln(x)} + \frac{46log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{2}(xln(x))} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(xln(x))ln(x)} + \frac{54log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln^{2}(x)} + \frac{90log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{3}(xln(x))} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(xln(x))ln^{2}(x)} + \frac{24log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(xln(x))ln^{3}(x)} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln^{4}(xln(x))} + \frac{12log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln^{2}(x)} + \frac{18log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))ln^{3}(x)} + \frac{90log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{3}(xln(x))} - \frac{18}{x^{3}ln(x)ln^{4}(xln(x))} - \frac{6}{x^{4}ln^{4}(xln(x))ln^{3}(x)} - \frac{6}{x^{3}ln^{4}(xln(x))ln^{3}(x)} - \frac{6}{x^{4}ln^{3}(xln(x))ln^{3}(x)} + \frac{4log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))ln^{3}(x)} + \frac{72log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{4}(xln(x))} + \frac{24log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(x)ln^{4}(xln(x))} - \frac{6}{x^{3}ln^{3}(xln(x))ln^{3}(x)} - \frac{2}{x^{4}ln^{2}(xln(x))ln^{3}(x)} - \frac{2}{x^{3}ln^{2}(xln(x))ln^{3}(x)} - \frac{24}{x^{3}ln^{3}(xln(x))} + \frac{11log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(x)ln(xln(x))} + \frac{12log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln(xln(x))} + \frac{48log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(x)ln^{2}(xln(x))} + \frac{22log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(x)ln^{2}(xln(x))} + \frac{36log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(x)ln^{3}(xln(x))} + \frac{22log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{2}(xln(x))} - \frac{24}{x^{4}ln^{4}(xln(x))} - \frac{22}{x^{4}ln^{2}(xln(x))} + \frac{36log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{3}(xln(x))} + \frac{6log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(x)ln(xln(x))} - \frac{24}{x^{3}ln^{4}(xln(x))} - \frac{8}{x^{3}ln^{2}(xln(x))} + \frac{24log_{xln(x)}^{xe^{x}}}{x^{4}ln(x)ln^{4}(xln(x))} + \frac{36log_{xln(x)}^{xe^{x}}}{x^{4}ln^{3}(xln(x))} - \frac{6}{x^{4}ln(xln(x))} - \frac{36}{x^{4}ln^{3}(xln(x))} + \frac{22log_{xln(x)}^{xe^{x}}}{x^{4}ln^{2}(xln(x))} + \frac{24log_{xln(x)}^{xe^{x}}}{x^{4}ln^{4}(xln(x))} + \frac{6log_{xln(x)}^{xe^{x}}}{x^{4}ln(xln(x))}\\ \end{split}\end{equation} \]