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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ lg(log_{ln(x)}^{lg(x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(log_{ln(x)}^{lg(x)})\right)}{dx}\\=&\frac{(\frac{(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{(ln(ln(x)))})}{ln{10}(log_{ln(x)}^{lg(x)})}\\=&\frac{1}{xlog(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{1}{xln(x)ln(ln(x))ln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{xlog(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{1}{xln(x)ln(ln(x))ln{10}}\right)}{dx}\\=&\frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{xln^{2}{10}ln(ln(x))lg(x)} + \frac{-2*0}{xlog(ln(x), lg(x))ln^{3}{10}ln(ln(x))lg(x)} + \frac{-1}{xlog(ln(x), lg(x))ln^{2}{10}ln^{2}(ln(x))(ln(x))(x)lg(x)} + \frac{-1}{xlog(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg^{2}(x)ln{10}(x)} - \frac{-1}{x^{2}ln(x)ln(ln(x))ln{10}} - \frac{-1}{xln^{2}(x)(x)ln(ln(x))ln{10}} - \frac{-1}{xln(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} - \frac{-0}{xln(x)ln(ln(x))ln^{2}{10}}\\=&\frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{1}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{1}{x^{2}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{1}{x^{2}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{1}{x^{2}ln(x)ln(ln(x))ln{10}} + \frac{1}{x^{2}ln^{2}(x)ln(ln(x))ln{10}} + \frac{1}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{1}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{1}{x^{2}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{1}{x^{2}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{1}{x^{2}ln(x)ln(ln(x))ln{10}} + \frac{1}{x^{2}ln^{2}(x)ln(ln(x))ln{10}} + \frac{1}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln{10}}\right)}{dx}\\=&\frac{--2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{2}ln^{2}{10}ln(ln(x))lg(x)} - \frac{-2*0}{x^{2}log(ln(x), lg(x))ln^{3}{10}ln(ln(x))lg(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln^{2}(ln(x))(ln(x))(x)lg(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{-3*0}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{-2}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{3}(ln(x))(ln(x))(x)lg^{2}(x)} - \frac{-2}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{3}(x)ln{10}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{2}ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}(x)(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{-2}{x^{2}log(ln(x), lg(x))ln(x)ln^{3}(ln(x))(ln(x))(x)ln^{2}{10}lg(x)} + \frac{-2*0}{x^{2}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg(x)} + \frac{-1}{x^{2}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{2}ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{-2*0}{x^{2}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln^{2}(x)(x)ln^{2}(ln(x))lg(x)} - \frac{-2}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{3}(ln(x))(ln(x))(x)lg(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{2}ln(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}(ln(x))(ln(x))(x)ln^{3}{10}lg^{2}(x)} - \frac{-3*0}{x^{2}log(ln(x), lg(x))ln(ln(x))ln^{4}{10}lg^{2}(x)} - \frac{-2}{x^{2}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{-2}{x^{3}ln(x)ln(ln(x))ln{10}} + \frac{-1}{x^{2}ln^{2}(x)(x)ln(ln(x))ln{10}} + \frac{-1}{x^{2}ln(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} + \frac{-0}{x^{2}ln(x)ln(ln(x))ln^{2}{10}} + \frac{-2}{x^{3}ln^{2}(x)ln(ln(x))ln{10}} + \frac{-2}{x^{2}ln^{3}(x)(x)ln(ln(x))ln{10}} + \frac{-1}{x^{2}ln^{2}(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} + \frac{-0}{x^{2}ln^{2}(x)ln(ln(x))ln^{2}{10}} + \frac{-2}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln{10}} + \frac{-2}{x^{2}ln^{3}(x)(x)ln^{2}(ln(x))ln{10}} + \frac{-2}{x^{2}ln^{2}(x)ln^{3}(ln(x))(ln(x))(x)ln{10}} + \frac{-0}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}}\\=&\frac{2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} + \frac{3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{3}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{3}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} - \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{1}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{3}(x)} - \frac{2}{x^{3}ln(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{2}(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln{10}} - \frac{2}{x^{3}ln^{3}(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln{10}} - \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} + \frac{3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{3}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{3}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} - \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{1}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{3}(x)} - \frac{2}{x^{3}ln(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{2}(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln{10}} - \frac{2}{x^{3}ln^{3}(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln{10}} - \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln{10}}\right)}{dx}\\=&\frac{2*-3}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} + \frac{2(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}{10}ln(ln(x))lg(x)} + \frac{2*-2*0}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(ln(x))lg(x)} + \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{2}(ln(x))(ln(x))(x)lg(x)} + \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{3(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{3*-3*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{3*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{3}(ln(x))(ln(x))(x)lg^{2}(x)} + \frac{3*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{3}(x)ln{10}(x)} - \frac{3*-3}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{3(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{3*-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{3*-2}{x^{3}log(ln(x), lg(x))ln(x)ln^{3}(ln(x))(ln(x))(x)ln^{2}{10}lg(x)} - \frac{3*-2*0}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg(x)} - \frac{3*-1}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3*-2*0}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{2}(x)(x)ln^{2}(ln(x))lg(x)} + \frac{3*-2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{3}(ln(x))(ln(x))(x)lg(x)} + \frac{3*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{3(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{3*-1}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))(ln(x))(x)ln^{3}{10}lg^{2}(x)} + \frac{3*-3*0}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{4}{10}lg^{2}(x)} + \frac{3*-2}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} + \frac{2(\frac{-3(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{4}(ln(ln(x)))})}{x^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} + \frac{2*-4*0}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{5}{10}ln^{3}(ln(x))lg^{3}(x)} + \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{4}(ln(x))(ln(x))(x)lg^{3}(x)} + \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{4}(x)ln{10}(x)} - \frac{2*-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{2(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{2*-1}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(x)(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{4}(ln(x))(ln(x))(x)ln^{3}{10}lg^{2}(x)} - \frac{2*-3*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{4}{10}lg^{2}(x)} - \frac{2*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2*-3*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2*-1}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(x)(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{4}(ln(x))(ln(x))(x)lg^{2}(x)} + \frac{2*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} + \frac{2(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} + \frac{2*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}(ln(x))(ln(x))(x)ln^{4}{10}lg^{3}(x)} + \frac{2*-4*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{5}{10}lg^{3}(x)} + \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{4}(x)ln{10}(x)} - \frac{2*-3}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{2(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{2*-2}{x^{3}log(ln(x), lg(x))ln^{3}(x)(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{2*-3}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{4}(ln(x))(ln(x))(x)ln^{2}{10}lg(x)} - \frac{2*-2*0}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{3}{10}lg(x)} - \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-3}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}(x)(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))(ln(x))(x)ln^{2}{10}lg(x)} - \frac{-2*0}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{3}{10}lg(x)} - \frac{-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-3}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} - \frac{-3*0}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{3}(ln(x))(ln(x))(x)ln(x)lg^{2}(x)} - \frac{-1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln^{2}(x)(x)lg^{2}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{3}(x)ln{10}(x)} + \frac{-3}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}(x)(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{-2*0}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}{10}ln^{2}(ln(x))lg(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{3}(ln(x))(ln(x))(x)lg(x)} + \frac{-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg^{2}(x)ln{10}(x)} + \frac{2*-3}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{2(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{2*-2*0}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{2*-3}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{4}(ln(x))(ln(x))(x)ln^{2}(x)lg(x)} + \frac{2*-2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{3}(x)(x)lg(x)} + \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg^{2}(x)ln{10}(x)} + \frac{-3}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{-3*0}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{-1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(x)(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{3}(ln(x))(ln(x))(x)lg^{2}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{3}(x)ln{10}(x)} + \frac{-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} + \frac{(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} + \frac{-4*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{5}{10}ln^{2}(ln(x))lg^{3}(x)} + \frac{-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{3}(ln(x))(ln(x))(x)lg^{3}(x)} + \frac{-3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{4}(x)ln{10}(x)} - \frac{-3}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln(x)ln^{3}(ln(x))(ln(x))(x)ln^{3}{10}lg^{2}(x)} - \frac{-3*0}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{4}{10}lg^{2}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{-3}{x^{4}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}(ln(x))(ln(x))(x)ln(x)ln^{3}{10}lg^{2}(x)} + \frac{-1}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln^{2}(x)(x)ln^{3}{10}lg^{2}(x)} + \frac{-3*0}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{4}{10}lg^{2}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{3}(x)} + \frac{2(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{4}{10}ln(ln(x))lg^{3}(x)} + \frac{2*-4*0}{x^{3}log(ln(x), lg(x))ln^{5}{10}ln(ln(x))lg^{3}(x)} + \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln^{2}(ln(x))(ln(x))(x)lg^{3}(x)} + \frac{2*-3}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{4}(x)ln{10}(x)} - \frac{2*-3}{x^{4}ln(x)ln(ln(x))ln{10}} - \frac{2*-1}{x^{3}ln^{2}(x)(x)ln(ln(x))ln{10}} - \frac{2*-1}{x^{3}ln(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} - \frac{2*-0}{x^{3}ln(x)ln(ln(x))ln^{2}{10}} - \frac{3*-3}{x^{4}ln^{2}(x)ln(ln(x))ln{10}} - \frac{3*-2}{x^{3}ln^{3}(x)(x)ln(ln(x))ln{10}} - \frac{3*-1}{x^{3}ln^{2}(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} - \frac{3*-0}{x^{3}ln^{2}(x)ln(ln(x))ln^{2}{10}} - \frac{3*-3}{x^{4}ln^{2}(x)ln^{2}(ln(x))ln{10}} - \frac{3*-2}{x^{3}ln^{3}(x)(x)ln^{2}(ln(x))ln{10}} - \frac{3*-2}{x^{3}ln^{2}(x)ln^{3}(ln(x))(ln(x))(x)ln{10}} - \frac{3*-0}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}} - \frac{2*-3}{x^{4}ln^{3}(x)ln(ln(x))ln{10}} - \frac{2*-3}{x^{3}ln^{4}(x)(x)ln(ln(x))ln{10}} - \frac{2*-1}{x^{3}ln^{3}(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} - \frac{2*-0}{x^{3}ln^{3}(x)ln(ln(x))ln^{2}{10}} - \frac{3*-3}{x^{4}ln^{3}(x)ln^{2}(ln(x))ln{10}} - \frac{3*-3}{x^{3}ln^{4}(x)(x)ln^{2}(ln(x))ln{10}} - \frac{3*-2}{x^{3}ln^{3}(x)ln^{3}(ln(x))(ln(x))(x)ln{10}} - \frac{3*-0}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln^{2}{10}} - \frac{2*-3}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln{10}} - \frac{2*-3}{x^{3}ln^{4}(x)(x)ln^{3}(ln(x))ln{10}} - \frac{2*-3}{x^{3}ln^{3}(x)ln^{4}(ln(x))(ln(x))(x)ln{10}} - \frac{2*-0}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{2}{10}}\\=&\frac{-6}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{11}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{11}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{11}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{11}{x^{4}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} + \frac{12}{x^{4}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} - \frac{12}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} + \frac{12}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} + \frac{6}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{6}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} - \frac{12}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} + \frac{6}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{3}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{4}ln^{5}{10}ln^{4}(ln(x))lg^{4}(x)} + \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{3}ln(x)ln^{4}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln(x)ln^{4}(ln(x))lg^{3}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{3}(ln(x))ln^{5}{10}lg^{4}(x)} + \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(x)ln^{4}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{4}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{3}(ln(x))ln(x)lg^{3}(x)} - \frac{2}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(x)ln^{3}{10}ln^{3}(ln(x))lg^{2}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{4}(ln(x))ln^{2}(x)lg^{2}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln(x)ln^{3}(ln(x))lg^{3}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{5}{10}ln^{3}(ln(x))lg^{4}(x)} + \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{4}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}(ln(x))ln(x)ln^{4}{10}lg^{3}(x)} - \frac{8}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{5}{10}ln^{2}(ln(x))lg^{4}(x)} + \frac{6}{x^{4}log(ln(x), lg(x))ln^{3}(x)ln^{4}(ln(x))ln^{2}{10}lg(x)} + \frac{4}{x^{4}log(ln(x), lg(x))ln^{3}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln^{3}(ln(x))ln^{2}(x)lg^{2}(x)} + \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln^{2}(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{1}{x^{4}log(ln(x), lg(x))ln^{2}(ln(x))ln^{3}{10}ln^{2}(x)lg^{2}(x)} + \frac{4}{x^{4}log(ln(x), lg(x))ln^{4}{10}ln^{2}(ln(x))ln(x)lg^{3}(x)} - \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln^{3}(x)ln^{4}(ln(x))lg(x)} - \frac{4}{x^{4}log(ln(x), lg(x))ln^{3}(ln(x))ln^{2}{10}ln^{3}(x)lg(x)} - \frac{1}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{4}{10}ln(x)ln^{2}(ln(x))lg^{3}(x)} - \frac{3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{5}{10}lg^{4}(x)} + \frac{2}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}(ln(x))ln^{2}(x)ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln(ln(x))ln^{5}{10}lg^{4}(x)} + \frac{6}{x^{4}ln(x)ln(ln(x))ln{10}} + \frac{11}{x^{4}ln^{2}(x)ln(ln(x))ln{10}} + \frac{11}{x^{4}ln^{2}(x)ln^{2}(ln(x))ln{10}} + \frac{12}{x^{4}ln^{3}(x)ln(ln(x))ln{10}} + \frac{18}{x^{4}ln^{3}(x)ln^{2}(ln(x))ln{10}} + \frac{12}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln{10}} + \frac{6}{x^{4}ln^{4}(x)ln(ln(x))ln{10}} + \frac{11}{x^{4}ln^{4}(x)ln^{2}(ln(x))ln{10}} + \frac{12}{x^{4}ln^{4}(x)ln^{3}(ln(x))ln{10}} + \frac{6}{x^{4}ln^{4}(x)ln^{4}(ln(x))ln{10}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ lg(log_{ln(x)}^{lg(x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(log_{ln(x)}^{lg(x)})\right)}{dx}\\=&\frac{(\frac{(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{(ln(ln(x)))})}{ln{10}(log_{ln(x)}^{lg(x)})}\\=&\frac{1}{xlog(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{1}{xln(x)ln(ln(x))ln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{xlog(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{1}{xln(x)ln(ln(x))ln{10}}\right)}{dx}\\=&\frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{xln^{2}{10}ln(ln(x))lg(x)} + \frac{-2*0}{xlog(ln(x), lg(x))ln^{3}{10}ln(ln(x))lg(x)} + \frac{-1}{xlog(ln(x), lg(x))ln^{2}{10}ln^{2}(ln(x))(ln(x))(x)lg(x)} + \frac{-1}{xlog(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg^{2}(x)ln{10}(x)} - \frac{-1}{x^{2}ln(x)ln(ln(x))ln{10}} - \frac{-1}{xln^{2}(x)(x)ln(ln(x))ln{10}} - \frac{-1}{xln(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} - \frac{-0}{xln(x)ln(ln(x))ln^{2}{10}}\\=&\frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{1}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{1}{x^{2}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{1}{x^{2}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{1}{x^{2}ln(x)ln(ln(x))ln{10}} + \frac{1}{x^{2}ln^{2}(x)ln(ln(x))ln{10}} + \frac{1}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{1}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{1}{x^{2}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{1}{x^{2}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{1}{x^{2}ln(x)ln(ln(x))ln{10}} + \frac{1}{x^{2}ln^{2}(x)ln(ln(x))ln{10}} + \frac{1}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln{10}}\right)}{dx}\\=&\frac{--2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{2}ln^{2}{10}ln(ln(x))lg(x)} - \frac{-2*0}{x^{2}log(ln(x), lg(x))ln^{3}{10}ln(ln(x))lg(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln^{2}(ln(x))(ln(x))(x)lg(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{-3*0}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{-2}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{3}(ln(x))(ln(x))(x)lg^{2}(x)} - \frac{-2}{x^{2}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{3}(x)ln{10}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{2}ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}(x)(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{-2}{x^{2}log(ln(x), lg(x))ln(x)ln^{3}(ln(x))(ln(x))(x)ln^{2}{10}lg(x)} + \frac{-2*0}{x^{2}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg(x)} + \frac{-1}{x^{2}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{2}ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{-2*0}{x^{2}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln^{2}(x)(x)ln^{2}(ln(x))lg(x)} - \frac{-2}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{3}(ln(x))(ln(x))(x)lg(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{2}ln(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{-1}{x^{2}log(ln(x), lg(x))ln^{2}(ln(x))(ln(x))(x)ln^{3}{10}lg^{2}(x)} - \frac{-3*0}{x^{2}log(ln(x), lg(x))ln(ln(x))ln^{4}{10}lg^{2}(x)} - \frac{-2}{x^{2}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{-2}{x^{3}ln(x)ln(ln(x))ln{10}} + \frac{-1}{x^{2}ln^{2}(x)(x)ln(ln(x))ln{10}} + \frac{-1}{x^{2}ln(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} + \frac{-0}{x^{2}ln(x)ln(ln(x))ln^{2}{10}} + \frac{-2}{x^{3}ln^{2}(x)ln(ln(x))ln{10}} + \frac{-2}{x^{2}ln^{3}(x)(x)ln(ln(x))ln{10}} + \frac{-1}{x^{2}ln^{2}(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} + \frac{-0}{x^{2}ln^{2}(x)ln(ln(x))ln^{2}{10}} + \frac{-2}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln{10}} + \frac{-2}{x^{2}ln^{3}(x)(x)ln^{2}(ln(x))ln{10}} + \frac{-2}{x^{2}ln^{2}(x)ln^{3}(ln(x))(ln(x))(x)ln{10}} + \frac{-0}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}}\\=&\frac{2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} + \frac{3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{3}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{3}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} - \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{1}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{3}(x)} - \frac{2}{x^{3}ln(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{2}(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln{10}} - \frac{2}{x^{3}ln^{3}(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln{10}} - \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} + \frac{3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{3}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{3}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} - \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{1}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} - \frac{1}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{1}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{3}(x)} - \frac{2}{x^{3}ln(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{2}(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln{10}} - \frac{2}{x^{3}ln^{3}(x)ln(ln(x))ln{10}} - \frac{3}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln{10}} - \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln{10}}\right)}{dx}\\=&\frac{2*-3}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} + \frac{2(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}{10}ln(ln(x))lg(x)} + \frac{2*-2*0}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(ln(x))lg(x)} + \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{2}(ln(x))(ln(x))(x)lg(x)} + \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{3(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{3*-3*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{3*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{3}(ln(x))(ln(x))(x)lg^{2}(x)} + \frac{3*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{3}(x)ln{10}(x)} - \frac{3*-3}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{3(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{3*-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{3*-2}{x^{3}log(ln(x), lg(x))ln(x)ln^{3}(ln(x))(ln(x))(x)ln^{2}{10}lg(x)} - \frac{3*-2*0}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg(x)} - \frac{3*-1}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3*-2*0}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg(x)} + \frac{3*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{2}(x)(x)ln^{2}(ln(x))lg(x)} + \frac{3*-2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{3}(ln(x))(ln(x))(x)lg(x)} + \frac{3*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{3(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{3*-1}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))(ln(x))(x)ln^{3}{10}lg^{2}(x)} + \frac{3*-3*0}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{4}{10}lg^{2}(x)} + \frac{3*-2}{x^{3}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} + \frac{2(\frac{-3(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{4}(ln(ln(x)))})}{x^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} + \frac{2*-4*0}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{5}{10}ln^{3}(ln(x))lg^{3}(x)} + \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{4}(ln(x))(ln(x))(x)lg^{3}(x)} + \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{4}(x)ln{10}(x)} - \frac{2*-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{2(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{2*-1}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(x)(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{4}(ln(x))(ln(x))(x)ln^{3}{10}lg^{2}(x)} - \frac{2*-3*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{4}{10}lg^{2}(x)} - \frac{2*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2*-3*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2*-1}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(x)(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{4}(ln(x))(ln(x))(x)lg^{2}(x)} + \frac{2*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} + \frac{2(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} + \frac{2*-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{3}(ln(x))(ln(x))(x)ln^{4}{10}lg^{3}(x)} + \frac{2*-4*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{5}{10}lg^{3}(x)} + \frac{2*-3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{4}(x)ln{10}(x)} - \frac{2*-3}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{2(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{2*-2}{x^{3}log(ln(x), lg(x))ln^{3}(x)(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{2*-3}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{4}(ln(x))(ln(x))(x)ln^{2}{10}lg(x)} - \frac{2*-2*0}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{3}{10}lg(x)} - \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-3}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}(x)(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))(ln(x))(x)ln^{2}{10}lg(x)} - \frac{-2*0}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{3}{10}lg(x)} - \frac{-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-3}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} - \frac{-3*0}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{3}(ln(x))(ln(x))(x)ln(x)lg^{2}(x)} - \frac{-1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln^{2}(x)(x)lg^{2}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{3}(x)ln{10}(x)} + \frac{-3}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}(x)(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} + \frac{-2*0}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{3}{10}ln^{2}(ln(x))lg(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{3}(ln(x))(ln(x))(x)lg(x)} + \frac{-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg^{2}(x)ln{10}(x)} + \frac{2*-3}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{2(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{2*-2*0}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} + \frac{2*-3}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{4}(ln(x))(ln(x))(x)ln^{2}(x)lg(x)} + \frac{2*-2}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{3}(x)(x)lg(x)} + \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg^{2}(x)ln{10}(x)} + \frac{-3}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{-3*0}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{-1}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln^{2}(x)(x)ln^{2}(ln(x))lg^{2}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{3}(ln(x))(ln(x))(x)lg^{2}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{3}(x)ln{10}(x)} + \frac{-3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} + \frac{(\frac{-2(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{3}(ln(ln(x)))})}{x^{3}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} + \frac{-4*0}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{5}{10}ln^{2}(ln(x))lg^{3}(x)} + \frac{-2}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{3}(ln(x))(ln(x))(x)lg^{3}(x)} + \frac{-3}{x^{3}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{4}(x)ln{10}(x)} - \frac{-3}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{-1}{x^{3}log(ln(x), lg(x))ln^{2}(x)(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln(x)ln^{3}(ln(x))(ln(x))(x)ln^{3}{10}lg^{2}(x)} - \frac{-3*0}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{4}{10}lg^{2}(x)} - \frac{-2}{x^{3}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{-3}{x^{4}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} + \frac{(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{3}(ln(x))(ln(x))(x)ln(x)ln^{3}{10}lg^{2}(x)} + \frac{-1}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln^{2}(x)(x)ln^{3}{10}lg^{2}(x)} + \frac{-3*0}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{4}{10}lg^{2}(x)} + \frac{-2}{x^{3}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{3}(x)} + \frac{2(\frac{-(\frac{(\frac{1}{ln{10}(x)})}{(lg(x))} - \frac{(\frac{1}{(x)})log_{ln(x)}^{lg(x)}}{(ln(x))})}{{\left(log(ln(x), lg(x))^{2}(ln(ln(x)))})}{x^{3}ln^{4}{10}ln(ln(x))lg^{3}(x)} + \frac{2*-4*0}{x^{3}log(ln(x), lg(x))ln^{5}{10}ln(ln(x))lg^{3}(x)} + \frac{2*-1}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln^{2}(ln(x))(ln(x))(x)lg^{3}(x)} + \frac{2*-3}{x^{3}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{4}(x)ln{10}(x)} - \frac{2*-3}{x^{4}ln(x)ln(ln(x))ln{10}} - \frac{2*-1}{x^{3}ln^{2}(x)(x)ln(ln(x))ln{10}} - \frac{2*-1}{x^{3}ln(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} - \frac{2*-0}{x^{3}ln(x)ln(ln(x))ln^{2}{10}} - \frac{3*-3}{x^{4}ln^{2}(x)ln(ln(x))ln{10}} - \frac{3*-2}{x^{3}ln^{3}(x)(x)ln(ln(x))ln{10}} - \frac{3*-1}{x^{3}ln^{2}(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} - \frac{3*-0}{x^{3}ln^{2}(x)ln(ln(x))ln^{2}{10}} - \frac{3*-3}{x^{4}ln^{2}(x)ln^{2}(ln(x))ln{10}} - \frac{3*-2}{x^{3}ln^{3}(x)(x)ln^{2}(ln(x))ln{10}} - \frac{3*-2}{x^{3}ln^{2}(x)ln^{3}(ln(x))(ln(x))(x)ln{10}} - \frac{3*-0}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}} - \frac{2*-3}{x^{4}ln^{3}(x)ln(ln(x))ln{10}} - \frac{2*-3}{x^{3}ln^{4}(x)(x)ln(ln(x))ln{10}} - \frac{2*-1}{x^{3}ln^{3}(x)ln^{2}(ln(x))(ln(x))(x)ln{10}} - \frac{2*-0}{x^{3}ln^{3}(x)ln(ln(x))ln^{2}{10}} - \frac{3*-3}{x^{4}ln^{3}(x)ln^{2}(ln(x))ln{10}} - \frac{3*-3}{x^{3}ln^{4}(x)(x)ln^{2}(ln(x))ln{10}} - \frac{3*-2}{x^{3}ln^{3}(x)ln^{3}(ln(x))(ln(x))(x)ln{10}} - \frac{3*-0}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln^{2}{10}} - \frac{2*-3}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln{10}} - \frac{2*-3}{x^{3}ln^{4}(x)(x)ln^{3}(ln(x))ln{10}} - \frac{2*-3}{x^{3}ln^{3}(x)ln^{4}(ln(x))(ln(x))(x)ln{10}} - \frac{2*-0}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{2}{10}}\\=&\frac{-6}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln(ln(x))lg(x)} - \frac{11}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} + \frac{11}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} - \frac{11}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln(x)ln^{2}(ln(x))lg(x)} - \frac{11}{x^{4}log(ln(x), lg(x))ln(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln^{3}(ln(x))lg^{3}(x)} + \frac{12}{x^{4}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln(x)ln^{3}(ln(x))lg^{2}(x)} - \frac{12}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} + \frac{12}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} + \frac{6}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{6}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln^{2}(ln(x))ln(x)lg^{2}(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} - \frac{12}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln^{3}(ln(x))ln^{2}(x)lg(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln(x)ln^{2}(ln(x))lg^{2}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{2}(ln(x))lg^{3}(x)} + \frac{6}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{2}(ln(x))ln(x)ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}log(ln(x), lg(x))ln^{4}{10}ln(ln(x))lg^{3}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{4}ln^{5}{10}ln^{4}(ln(x))lg^{4}(x)} + \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{3}ln(x)ln^{4}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{4}{10}ln(x)ln^{4}(ln(x))lg^{3}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{3}(ln(x))ln^{5}{10}lg^{4}(x)} + \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(x)ln^{4}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} + \frac{4}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln^{3}(ln(x))ln(x)lg^{3}(x)} - \frac{2}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(x)ln^{3}{10}ln^{3}(ln(x))lg^{2}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}{10}ln^{4}(ln(x))ln^{2}(x)lg^{2}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{4}{10}ln(x)ln^{3}(ln(x))lg^{3}(x)} - \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{3}ln^{5}{10}ln^{3}(ln(x))lg^{4}(x)} + \frac{6}{x^{4}{\left(log(ln(x), lg(x))^{2}ln(x)ln^{3}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{4}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{3}(ln(x))ln(x)ln^{4}{10}lg^{3}(x)} - \frac{8}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{5}{10}ln^{2}(ln(x))lg^{4}(x)} + \frac{6}{x^{4}log(ln(x), lg(x))ln^{3}(x)ln^{4}(ln(x))ln^{2}{10}lg(x)} + \frac{4}{x^{4}log(ln(x), lg(x))ln^{3}(x)ln^{3}(ln(x))ln^{2}{10}lg(x)} - \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln^{3}(ln(x))ln^{2}(x)lg^{2}(x)} + \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}(x)ln^{2}(ln(x))ln^{2}{10}lg(x)} + \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}{10}ln^{2}(x)ln^{3}(ln(x))lg^{2}(x)} + \frac{1}{x^{4}log(ln(x), lg(x))ln^{2}(ln(x))ln^{3}{10}ln^{2}(x)lg^{2}(x)} + \frac{4}{x^{4}log(ln(x), lg(x))ln^{4}{10}ln^{2}(ln(x))ln(x)lg^{3}(x)} - \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}(x)ln^{2}{10}ln^{2}(ln(x))lg(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{2}{10}ln^{3}(x)ln^{4}(ln(x))lg(x)} - \frac{4}{x^{4}log(ln(x), lg(x))ln^{3}(ln(x))ln^{2}{10}ln^{3}(x)lg(x)} - \frac{1}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{3}{10}ln^{2}(ln(x))lg^{2}(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln^{4}{10}ln(x)ln^{2}(ln(x))lg^{3}(x)} - \frac{3}{x^{4}{\left(log(ln(x), lg(x))^{2}ln^{2}(ln(x))ln^{5}{10}lg^{4}(x)} + \frac{2}{x^{4}log(ln(x), lg(x))ln^{2}(x)ln^{3}(ln(x))ln^{3}{10}lg^{2}(x)} - \frac{2}{x^{4}log(ln(x), lg(x))ln^{3}(ln(x))ln^{2}(x)ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{4}log(ln(x), lg(x))ln(x)ln^{2}(ln(x))ln^{4}{10}lg^{3}(x)} - \frac{6}{x^{4}log(ln(x), lg(x))ln(ln(x))ln^{5}{10}lg^{4}(x)} + \frac{6}{x^{4}ln(x)ln(ln(x))ln{10}} + \frac{11}{x^{4}ln^{2}(x)ln(ln(x))ln{10}} + \frac{11}{x^{4}ln^{2}(x)ln^{2}(ln(x))ln{10}} + \frac{12}{x^{4}ln^{3}(x)ln(ln(x))ln{10}} + \frac{18}{x^{4}ln^{3}(x)ln^{2}(ln(x))ln{10}} + \frac{12}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln{10}} + \frac{6}{x^{4}ln^{4}(x)ln(ln(x))ln{10}} + \frac{11}{x^{4}ln^{4}(x)ln^{2}(ln(x))ln{10}} + \frac{12}{x^{4}ln^{4}(x)ln^{3}(ln(x))ln{10}} + \frac{6}{x^{4}ln^{4}(x)ln^{4}(ln(x))ln{10}}\\ \end{split}\end{equation} \]