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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {{{x}^{x}}^{x}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{{x}^{x}}^{x}}^{x}\right)}{dx}\\=&({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))\\=&{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + x{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + x^{2}{{{x}^{x}}^{x}}^{x}ln(x) + x^{2}{{{x}^{x}}^{x}}^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + x{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + x^{2}{{{x}^{x}}^{x}}^{x}ln(x) + x^{2}{{{x}^{x}}^{x}}^{x}\right)}{dx}\\=&({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x}) + \frac{{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + {{{x}^{x}}^{x}}^{x}ln({x}^{x}) + x({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x}) + \frac{x{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 2x{{{x}^{x}}^{x}}^{x}ln(x) + x^{2}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x) + \frac{x^{2}{{{x}^{x}}^{x}}^{x}}{(x)} + 2x{{{x}^{x}}^{x}}^{x} + x^{2}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))\\=&{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x}) + x{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x}) + x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 2{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + 2x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + 2x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + 4x{{{x}^{x}}^{x}}^{x}ln(x) + 2x^{4}{{{x}^{x}}^{x}}^{x}ln(x) + 5x{{{x}^{x}}^{x}}^{x} + x^{4}{{{x}^{x}}^{x}}^{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x}) + x{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x}) + x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 2{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + 2x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + 2x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + 4x{{{x}^{x}}^{x}}^{x}ln(x) + 2x^{4}{{{x}^{x}}^{x}}^{x}ln(x) + 5x{{{x}^{x}}^{x}}^{x} + x^{4}{{{x}^{x}}^{x}}^{x}\right)}{dx}\\=&({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{2}({{x}^{x}}^{x}) + \frac{{{{x}^{x}}^{x}}^{x}*2ln({{x}^{x}}^{x})({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + {{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x}) + x({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x})ln({{x}^{x}}^{x}) + \frac{x{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln({{x}^{x}}^{x})}{({x}^{x})} + \frac{x{{{x}^{x}}^{x}}^{x}ln({x}^{x})({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + 2x{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + x^{2}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x)ln({{x}^{x}}^{x}) + \frac{x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})}{(x)} + \frac{x^{2}{{{x}^{x}}^{x}}^{x}ln(x)({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + 3x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x)ln({x}^{x}) + \frac{x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})}{(x)} + \frac{x^{3}{{{x}^{x}}^{x}}^{x}ln(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 2({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x}) + \frac{2{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + {{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x}) + x({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x})ln({x}^{x}) + \frac{x{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{({{x}^{x}}^{x})} + \frac{x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 3x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x})ln(x) + \frac{x^{3}{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{({x}^{x})} + \frac{x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})}{(x)} + 2x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + x^{2}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x})ln(x) + \frac{x^{2}{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{({{x}^{x}}^{x})} + \frac{x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})}{(x)} + 2*2x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + 2x^{2}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x}) + \frac{2x^{2}{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + 4x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + x^{4}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{2}(x) + \frac{x^{4}{{{x}^{x}}^{x}}^{x}*2ln(x)}{(x)} + 2*3x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 2x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x}) + \frac{2x^{3}{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 2x{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + x^{2}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{2}({x}^{x}) + \frac{x^{2}{{{x}^{x}}^{x}}^{x}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 4{{{x}^{x}}^{x}}^{x}ln(x) + 4x({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x) + \frac{4x{{{x}^{x}}^{x}}^{x}}{(x)} + 2*4x^{3}{{{x}^{x}}^{x}}^{x}ln(x) + 2x^{4}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x) + \frac{2x^{4}{{{x}^{x}}^{x}}^{x}}{(x)} + 5{{{x}^{x}}^{x}}^{x} + 5x({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})})) + 4x^{3}{{{x}^{x}}^{x}}^{x} + x^{4}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))\\=&3{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x)ln({{x}^{x}}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x})ln({{x}^{x}}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x})ln({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x)ln({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x})ln(x) + 3{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x})ln(x) + x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({{x}^{x}}^{x}) + 2x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({{x}^{x}}^{x}) + 9x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 9x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + x{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}({{x}^{x}}^{x}) + 2x^{5}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({x}^{x}) + 6x{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + 2x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln(x) + 2x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln(x) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + 3x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x}) + 3x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x}) + 3x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + 2x{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln({x}^{x}) + 2x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln({{x}^{x}}^{x}) + 6x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}(x) + {{{x}^{x}}^{x}}^{x}ln^{3}({{x}^{x}}^{x}) + 3x^{5}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + 6{{{x}^{x}}^{x}}^{x}ln(x) + 11{{{x}^{x}}^{x}}^{x} + x^{4}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({x}^{x}) + x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}(x) + x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}({x}^{x}) + 21x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 27x^{3}{{{x}^{x}}^{x}}^{x}ln(x) + 3x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x}) + 12x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + x^{6}{{{x}^{x}}^{x}}^{x}ln^{3}(x) + 15x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + 3x^{6}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + 6x{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln^{3}({x}^{x}) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + 3x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 3x^{6}{{{x}^{x}}^{x}}^{x}ln(x) + 15x^{3}{{{x}^{x}}^{x}}^{x} + x^{6}{{{x}^{x}}^{x}}^{x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 3{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x)ln({{x}^{x}}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x})ln({{x}^{x}}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x})ln({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x)ln({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x})ln(x) + 3{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x})ln(x) + x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({{x}^{x}}^{x}) + 2x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({{x}^{x}}^{x}) + 9x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 9x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + x{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}({{x}^{x}}^{x}) + 2x^{5}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({x}^{x}) + 6x{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + 2x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln(x) + 2x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln(x) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + 3x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x}) + 3x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x}) + 3x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + 2x{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln({x}^{x}) + 2x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln({{x}^{x}}^{x}) + 6x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}(x) + {{{x}^{x}}^{x}}^{x}ln^{3}({{x}^{x}}^{x}) + 3x^{5}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + 6{{{x}^{x}}^{x}}^{x}ln(x) + 11{{{x}^{x}}^{x}}^{x} + x^{4}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({x}^{x}) + x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}(x) + x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}({x}^{x}) + 21x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 27x^{3}{{{x}^{x}}^{x}}^{x}ln(x) + 3x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x}) + 12x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + x^{6}{{{x}^{x}}^{x}}^{x}ln^{3}(x) + 15x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + 3x^{6}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + 6x{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln^{3}({x}^{x}) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + 3x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 3x^{6}{{{x}^{x}}^{x}}^{x}ln(x) + 15x^{3}{{{x}^{x}}^{x}}^{x} + x^{6}{{{x}^{x}}^{x}}^{x}\right)}{dx}\\=&3({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x})ln({{x}^{x}}^{x}) + \frac{3{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln({{x}^{x}}^{x})}{({x}^{x})} + \frac{3{{{x}^{x}}^{x}}^{x}ln({x}^{x})({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + 3x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x)ln({{x}^{x}}^{x}) + x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x})ln(x)ln({{x}^{x}}^{x}) + \frac{x^{3}{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)ln({{x}^{x}}^{x})}{({x}^{x})} + \frac{x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x})}{(x)} + \frac{x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x)({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + 3x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x})ln({{x}^{x}}^{x}) + x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + 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\frac{x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 3x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x)ln({x}^{x}) + x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x})ln(x)ln({x}^{x}) + \frac{x^{3}{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)ln({x}^{x})}{({{x}^{x}}^{x})} + \frac{x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x})}{(x)} + \frac{x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 3x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x})ln(x) + x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x})ln({{x}^{x}}^{x})ln(x) + \frac{x^{3}{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln({{x}^{x}}^{x})ln(x)}{({x}^{x})} + \frac{x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{({{x}^{x}}^{x})} + \frac{x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x})}{(x)} + 3({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x})ln({x}^{x}) + \frac{3{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{({{x}^{x}}^{x})} + \frac{3{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 3x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x})ln(x) + x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + 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\frac{6x{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{({{x}^{x}}^{x})} + \frac{6x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})}{(x)} + 5x^{4}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}(x) + x^{5}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x})ln^{2}(x) + \frac{x^{5}{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{({x}^{x})} + \frac{x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})*2ln(x)}{(x)} + ({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{3}({{x}^{x}}^{x}) + \frac{{{{x}^{x}}^{x}}^{x}*3ln^{2}({{x}^{x}}^{x})({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + 3*5x^{4}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 3x^{5}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x)ln({x}^{x}) + \frac{3x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})}{(x)} + \frac{3x^{5}{{{x}^{x}}^{x}}^{x}ln(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 3*4x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + 3x^{4}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x})ln(x) + \frac{3x^{4}{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{({{x}^{x}}^{x})} + \frac{3x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})}{(x)} + 6({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x) + \frac{6{{{x}^{x}}^{x}}^{x}}{(x)} + 11({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})})) + 4x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({x}^{x}) + x^{4}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x)ln^{2}({x}^{x}) + \frac{x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})}{(x)} + \frac{x^{4}{{{x}^{x}}^{x}}^{x}ln(x)*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 4x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}(x) + x^{4}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x})ln^{2}(x) + \frac{x^{4}{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)}{({{x}^{x}}^{x})} + \frac{x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})*2ln(x)}{(x)} + 2x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}({x}^{x}) + x^{2}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x})ln^{2}({x}^{x}) + \frac{x^{2}{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}({x}^{x})}{({{x}^{x}}^{x})} + \frac{x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 21*2x{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 21x^{2}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x}) + \frac{21x^{2}{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 27*3x^{2}{{{x}^{x}}^{x}}^{x}ln(x) + 27x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x) + \frac{27x^{3}{{{x}^{x}}^{x}}^{x}}{(x)} + 3*2x{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x}) + 3x^{2}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{2}({{x}^{x}}^{x}) + \frac{3x^{2}{{{x}^{x}}^{x}}^{x}*2ln({{x}^{x}}^{x})({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + 12*3x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + 12x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{2}(x) + \frac{12x^{3}{{{x}^{x}}^{x}}^{x}*2ln(x)}{(x)} + 6x^{5}{{{x}^{x}}^{x}}^{x}ln^{3}(x) + x^{6}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{3}(x) + \frac{x^{6}{{{x}^{x}}^{x}}^{x}*3ln^{2}(x)}{(x)} + 15{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + 15x({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x}) + \frac{15x{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + 3*4x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + 3x^{4}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{2}({x}^{x}) + \frac{3x^{4}{{{x}^{x}}^{x}}^{x}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 3*6x^{5}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + 3x^{6}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{2}(x) + \frac{3x^{6}{{{x}^{x}}^{x}}^{x}*2ln(x)}{(x)} + 6{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + 6x({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{2}({x}^{x}) + \frac{6x{{{x}^{x}}^{x}}^{x}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 3x^{2}{{{x}^{x}}^{x}}^{x}ln^{3}({x}^{x}) + x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln^{3}({x}^{x}) + \frac{x^{3}{{{x}^{x}}^{x}}^{x}*3ln^{2}({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 3*4x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + 3x^{4}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({{x}^{x}}^{x}) + \frac{3x^{4}{{{x}^{x}}^{x}}^{x}({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{({{x}^{x}}^{x})} + 3*5x^{4}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 3x^{5}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln({x}^{x}) + \frac{3x^{5}{{{x}^{x}}^{x}}^{x}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{({x}^{x})} + 3*6x^{5}{{{x}^{x}}^{x}}^{x}ln(x) + 3x^{6}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))ln(x) + \frac{3x^{6}{{{x}^{x}}^{x}}^{x}}{(x)} + 15*3x^{2}{{{x}^{x}}^{x}}^{x} + 15x^{3}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})})) + 6x^{5}{{{x}^{x}}^{x}}^{x} + x^{6}({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})}))\\=&8{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln({x}^{x}) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln(x)ln({{x}^{x}}^{x}) + 12x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x})ln({{x}^{x}}^{x}) + 12x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x})ln({x}^{x}) + 12{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + 4{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}({{x}^{x}}^{x}) + 12{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + 3x^{5}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({x}^{x})ln({{x}^{x}}^{x}) + 3x^{5}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({{x}^{x}}^{x})ln({x}^{x}) + 9x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x)ln({{x}^{x}}^{x}) + 3x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln({x}^{x})ln(x) + 15x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x})ln(x) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln({{x}^{x}}^{x})ln(x) + x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x)ln^{2}({{x}^{x}}^{x}) + 4x^{5}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x})ln({{x}^{x}}^{x}) + 3x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln(x)ln({x}^{x}) + 4x^{5}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x)ln({x}^{x}) + 4x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x)ln({{x}^{x}}^{x}) + 4x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x})ln(x) + 12x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x)ln({x}^{x}) + 2x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}(x)ln({{x}^{x}}^{x}) + 12x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x})ln(x) + 4x^{5}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x})ln({x}^{x}) + 4x^{5}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x})ln(x) + 2x^{5}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}(x)ln({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x})ln^{2}({{x}^{x}}^{x}) + 2x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({{x}^{x}}^{x})ln({x}^{x}) + 2x^{4}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({x}^{x})ln({{x}^{x}}^{x}) + x^{4}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x})ln^{2}({x}^{x}) + 2x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}({x}^{x})ln(x) + x^{5}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x})ln^{2}(x) + 2x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}({{x}^{x}}^{x})ln(x) + x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x)ln^{2}({x}^{x}) + x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x})ln^{2}(x) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln^{2}({{x}^{x}}^{x}) + 3x^{6}{{{x}^{x}}^{x}}^{x}ln^{3}(x)ln({{x}^{x}}^{x}) + 66x^{4}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 54x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + 40x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({x}^{x}) + 3x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln^{2}(x) + 36x{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 66x^{4}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + 32x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({{x}^{x}}^{x}) + 36x{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + 8x{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({{x}^{x}}^{x}) + 3x^{7}{{{x}^{x}}^{x}}^{x}ln^{3}(x)ln({x}^{x}) + 3x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln^{2}({{x}^{x}}^{x}) + 3x^{6}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln^{2}({x}^{x}) + 3x{{{x}^{x}}^{x}}^{x}ln^{3}({{x}^{x}}^{x})ln({x}^{x}) + 8x^{6}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({{x}^{x}}^{x}) + 42x^{2}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x}) + 3x^{6}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln^{2}(x) + 54x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + 8x^{7}{{{x}^{x}}^{x}}^{x}ln^{2}(x)ln({x}^{x}) + 16x{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln(x) + 32x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln(x) + 3x^{5}{{{x}^{x}}^{x}}^{x}ln^{3}({x}^{x})ln(x) + 42x^{2}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x}) + 16x^{3}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({x}^{x}) + 16x{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln({{x}^{x}}^{x}) + 8x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln({{x}^{x}}^{x}) + 20x^{4}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}(x) + 8x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln(x) + 8x^{6}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x})ln(x) + 6x^{5}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln({{x}^{x}}^{x}) + 6x^{7}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln(x) + 8x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln({x}^{x}) + 3x^{3}{{{x}^{x}}^{x}}^{x}ln^{3}({x}^{x})ln({{x}^{x}}^{x}) + x{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{3}({{x}^{x}}^{x}) + 16x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}(x) + 12{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + 4x^{4}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({{x}^{x}}^{x}) + 8x{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}({x}^{x}) + 3x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x})ln^{2}({x}^{x}) + 4x^{7}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}(x) + x^{2}{{{x}^{x}}^{x}}^{x}ln(x)ln^{3}({{x}^{x}}^{x}) + 44{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + 4x^{3}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{2}({{x}^{x}}^{x}) + 6x^{7}{{{x}^{x}}^{x}}^{x}ln(x)ln({x}^{x}) + 3x^{2}{{{x}^{x}}^{x}}^{x}ln^{3}({{x}^{x}}^{x})ln(x) + 6x^{6}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln(x) + 6x^{6}{{{x}^{x}}^{x}}^{x}ln(x)ln({{x}^{x}}^{x}) + {{{x}^{x}}^{x}}^{x}ln^{4}({{x}^{x}}^{x}) + 4x^{6}{{{x}^{x}}^{x}}^{x}ln(x)ln^{2}({x}^{x}) + 4x^{6}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}(x) + 6x^{5}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln({x}^{x}) + 4x^{4}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{2}({x}^{x}) + x^{6}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{3}(x) + x^{7}{{{x}^{x}}^{x}}^{x}ln({x}^{x})ln^{3}(x) + x^{5}{{{x}^{x}}^{x}}^{x}ln(x)ln^{3}({x}^{x}) + x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x})ln^{3}({x}^{x}) + 4x^{2}{{{x}^{x}}^{x}}^{x}ln^{3}({{x}^{x}}^{x}) + 72x^{4}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 188x^{2}{{{x}^{x}}^{x}}^{x}ln(x) + 72x^{2}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + 104x{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 30x{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x}) + 54x^{3}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + 78x^{5}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + 24x^{5}{{{x}^{x}}^{x}}^{x}ln^{3}(x) + 60x^{3}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + x^{8}{{{x}^{x}}^{x}}^{x}ln^{4}(x) + 84x^{5}{{{x}^{x}}^{x}}^{x}ln(x) + 4x^{8}{{{x}^{x}}^{x}}^{x}ln^{3}(x) + 6x^{8}{{{x}^{x}}^{x}}^{x}ln^{2}(x) + 12x^{2}{{{x}^{x}}^{x}}^{x}ln^{3}({x}^{x}) + 4x^{5}{{{x}^{x}}^{x}}^{x}ln^{3}({x}^{x}) + 6x^{6}{{{x}^{x}}^{x}}^{x}ln^{2}({x}^{x}) + 6x^{4}{{{x}^{x}}^{x}}^{x}ln^{2}({{x}^{x}}^{x}) + x^{4}{{{x}^{x}}^{x}}^{x}ln^{4}({x}^{x}) + 4x^{6}{{{x}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + 4x^{7}{{{x}^{x}}^{x}}^{x}ln({x}^{x}) + 4x^{8}{{{x}^{x}}^{x}}^{x}ln(x) + 119x^{2}{{{x}^{x}}^{x}}^{x} + \frac{6{{{x}^{x}}^{x}}^{x}}{x} + 30x^{5}{{{x}^{x}}^{x}}^{x} + x^{8}{{{x}^{x}}^{x}}^{x}\\ \end{split}\end{equation} \]