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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {{(e^{x})}^{e^{x}}}^{e^{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {{e^{x}}^{e^{x}}}^{e^{x}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{e^{x}}^{e^{x}}}^{e^{x}}\right)}{dx}\\=&({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))\\=&{{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}\right)}{dx}\\=&({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{x}ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{x}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{2}}ln(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}*2e^{x}e^{x}ln(e^{x}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}e^{x}}{(e^{x})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{2}} + {{e^{x}}^{e^{x}}}^{e^{x}}*2e^{x}e^{x}\\=&{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}})ln(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln(e^{x})ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln(e^{x}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln^{2}({e^{x}}^{e^{x}}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln(e^{x}) + 4{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}} + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}})ln(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln(e^{x})ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln(e^{x}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln^{2}({e^{x}}^{e^{x}}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln(e^{x}) + 4{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}} + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}\right)}{dx}\\=&({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{3}}ln({e^{x}}^{e^{x}})ln(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}*3e^{{x}*{2}}e^{x}ln({e^{x}}^{e^{x}})ln(e^{x}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))ln(e^{x})}{({e^{x}}^{e^{x}})} + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}})e^{x}}{(e^{x})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{3}}ln(e^{x})ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}*3e^{{x}*{2}}e^{x}ln(e^{x})ln({e^{x}}^{e^{x}}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}e^{x}ln({e^{x}}^{e^{x}})}{(e^{x})} + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln(e^{x})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{4}}ln^{2}(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}*4e^{{x}*{3}}e^{x}ln^{2}(e^{x}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}*2ln(e^{x})e^{x}}{(e^{x})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{x}ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{x}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + 3({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{2}}ln(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}*2e^{x}e^{x}ln(e^{x}) + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}e^{x}}{(e^{x})} + 2({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{3}}ln({e^{x}}^{e^{x}}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}*3e^{{x}*{2}}e^{x}ln({e^{x}}^{e^{x}}) + \frac{2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{2}}ln^{2}({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}*2e^{x}e^{x}ln^{2}({e^{x}}^{e^{x}}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}*2ln({e^{x}}^{e^{x}})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + 2({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{4}}ln(e^{x}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}*4e^{{x}*{3}}e^{x}ln(e^{x}) + \frac{2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}e^{x}}{(e^{x})} + 4({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{2}} + 4{{e^{x}}^{e^{x}}}^{e^{x}}*2e^{x}e^{x} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{4}} + {{e^{x}}^{e^{x}}}^{e^{x}}*4e^{{x}*{3}}e^{x}\\=&2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}({e^{x}}^{e^{x}})ln(e^{x}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln^{2}(e^{x})ln({e^{x}}^{e^{x}}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}})ln(e^{x}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln(e^{x})ln({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}})ln(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln(e^{x})ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}})ln^{2}(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln(e^{x})ln^{2}({e^{x}}^{e^{x}}) + 9{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}(e^{x}) + 21{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln^{2}({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + 7{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{3}(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{2}(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}({e^{x}}^{e^{x}}) + 15{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln^{3}({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln(e^{x}) + 12{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}} + 12{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}} + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}({e^{x}}^{e^{x}})ln(e^{x}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln^{2}(e^{x})ln({e^{x}}^{e^{x}}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}})ln(e^{x}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln(e^{x})ln({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}})ln(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln(e^{x})ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}})ln^{2}(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln(e^{x})ln^{2}({e^{x}}^{e^{x}}) + 9{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}(e^{x}) + 21{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln^{2}({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + 7{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{3}(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{2}(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}({e^{x}}^{e^{x}}) + 15{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln^{3}({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln(e^{x}) + 12{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}} + 12{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}} + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}\right)}{dx}\\=&2({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{4}}ln^{2}({e^{x}}^{e^{x}})ln(e^{x}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}*4e^{{x}*{3}}e^{x}ln^{2}({e^{x}}^{e^{x}})ln(e^{x}) + \frac{2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}*2ln({e^{x}}^{e^{x}})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))ln(e^{x})}{({e^{x}}^{e^{x}})} + \frac{2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}({e^{x}}^{e^{x}})e^{x}}{(e^{x})} + 2({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{5}}ln^{2}(e^{x})ln({e^{x}}^{e^{x}}) + 2{{e^{x}}^{e^{x}}}^{e^{x}}*5e^{{x}*{4}}e^{x}ln^{2}(e^{x})ln({e^{x}}^{e^{x}}) + \frac{2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}*2ln(e^{x})e^{x}ln({e^{x}}^{e^{x}})}{(e^{x})} + \frac{2{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln^{2}(e^{x})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + 6({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{3}}ln({e^{x}}^{e^{x}})ln(e^{x}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}*3e^{{x}*{2}}e^{x}ln({e^{x}}^{e^{x}})ln(e^{x}) + \frac{6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))ln(e^{x})}{({e^{x}}^{e^{x}})} + \frac{6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}})e^{x}}{(e^{x})} + 6({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{3}}ln(e^{x})ln({e^{x}}^{e^{x}}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}*3e^{{x}*{2}}e^{x}ln(e^{x})ln({e^{x}}^{e^{x}}) + \frac{6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}e^{x}ln({e^{x}}^{e^{x}})}{(e^{x})} + \frac{6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln(e^{x})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + 3({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{5}}ln({e^{x}}^{e^{x}})ln(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}*5e^{{x}*{4}}e^{x}ln({e^{x}}^{e^{x}})ln(e^{x}) + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))ln(e^{x})}{({e^{x}}^{e^{x}})} + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}})e^{x}}{(e^{x})} + 3({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{5}}ln(e^{x})ln({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}*5e^{{x}*{4}}e^{x}ln(e^{x})ln({e^{x}}^{e^{x}}) + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}e^{x}ln({e^{x}}^{e^{x}})}{(e^{x})} + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln(e^{x})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{5}}ln({e^{x}}^{e^{x}})ln^{2}(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}*5e^{{x}*{4}}e^{x}ln({e^{x}}^{e^{x}})ln^{2}(e^{x}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))ln^{2}(e^{x})}{({e^{x}}^{e^{x}})} + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}})*2ln(e^{x})e^{x}}{(e^{x})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{4}}ln(e^{x})ln^{2}({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}*4e^{{x}*{3}}e^{x}ln(e^{x})ln^{2}({e^{x}}^{e^{x}}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}e^{x}ln^{2}({e^{x}}^{e^{x}})}{(e^{x})} + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln(e^{x})*2ln({e^{x}}^{e^{x}})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + 9({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{4}}ln^{2}(e^{x}) + 9{{e^{x}}^{e^{x}}}^{e^{x}}*4e^{{x}*{3}}e^{x}ln^{2}(e^{x}) + \frac{9{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}*2ln(e^{x})e^{x}}{(e^{x})} + 21({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{4}}ln(e^{x}) + 21{{e^{x}}^{e^{x}}}^{e^{x}}*4e^{{x}*{3}}e^{x}ln(e^{x}) + \frac{21{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}e^{x}}{(e^{x})} + 3({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{2}}ln^{2}({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}*2e^{x}e^{x}ln^{2}({e^{x}}^{e^{x}}) + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}*2ln({e^{x}}^{e^{x}})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{x}ln({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{x}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + 7({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{2}}ln(e^{x}) + 7{{e^{x}}^{e^{x}}}^{e^{x}}*2e^{x}e^{x}ln(e^{x}) + \frac{7{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}e^{x}}{(e^{x})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{6}}ln^{3}(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}*6e^{{x}*{5}}e^{x}ln^{3}(e^{x}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}*3ln^{2}(e^{x})e^{x}}{(e^{x})} + 3({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{6}}ln^{2}(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}*6e^{{x}*{5}}e^{x}ln^{2}(e^{x}) + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}*2ln(e^{x})e^{x}}{(e^{x})} + 3({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{4}}ln^{2}({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}*4e^{{x}*{3}}e^{x}ln^{2}({e^{x}}^{e^{x}}) + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}*2ln({e^{x}}^{e^{x}})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + 15({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{3}}ln({e^{x}}^{e^{x}}) + 15{{e^{x}}^{e^{x}}}^{e^{x}}*3e^{{x}*{2}}e^{x}ln({e^{x}}^{e^{x}}) + \frac{15{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + 3({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{5}}ln({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}*5e^{{x}*{4}}e^{x}ln({e^{x}}^{e^{x}}) + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{3}}ln^{3}({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}*3e^{{x}*{2}}e^{x}ln^{3}({e^{x}}^{e^{x}}) + \frac{{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}*3ln^{2}({e^{x}}^{e^{x}})({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})}))}{({e^{x}}^{e^{x}})} + 3({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{6}}ln(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}*6e^{{x}*{5}}e^{x}ln(e^{x}) + \frac{3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}e^{x}}{(e^{x})} + 12({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{2}} + 12{{e^{x}}^{e^{x}}}^{e^{x}}*2e^{x}e^{x} + 12({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{4}} + 12{{e^{x}}^{e^{x}}}^{e^{x}}*4e^{{x}*{3}}e^{x} + ({{e^{x}}^{e^{x}}}^{e^{x}}((e^{x})ln({e^{x}}^{e^{x}}) + \frac{(e^{x})(({e^{x}}^{e^{x}}((e^{x})ln(e^{x}) + \frac{(e^{x})(e^{x})}{(e^{x})})))}{({e^{x}}^{e^{x}})}))e^{{x}*{6}} + {{e^{x}}^{e^{x}}}^{e^{x}}*6e^{{x}*{5}}e^{x}\\=&3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln^{3}({e^{x}}^{e^{x}})ln(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{2}(e^{x})ln^{2}({e^{x}}^{e^{x}}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{7}}ln^{3}(e^{x})ln({e^{x}}^{e^{x}}) + 20{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}({e^{x}}^{e^{x}})ln(e^{x}) + 28{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln^{2}(e^{x})ln({e^{x}}^{e^{x}}) + 48{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}})ln(e^{x}) + 3{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{2}({e^{x}}^{e^{x}})ln^{2}(e^{x}) + 48{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln(e^{x})ln({e^{x}}^{e^{x}}) + 25{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}})ln(e^{x}) + 8{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{7}}ln^{2}(e^{x})ln({e^{x}}^{e^{x}}) + 25{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln(e^{x})ln({e^{x}}^{e^{x}}) + 8{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{2}({e^{x}}^{e^{x}})ln(e^{x}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{7}}ln({e^{x}}^{e^{x}})ln(e^{x}) + 14{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}})ln^{2}(e^{x}) + 10{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln(e^{x})ln^{2}({e^{x}}^{e^{x}}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{7}}ln(e^{x})ln({e^{x}}^{e^{x}}) + 4{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{7}}ln({e^{x}}^{e^{x}})ln^{2}(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{7}}ln({e^{x}}^{e^{x}})ln^{3}(e^{x}) + 4{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln(e^{x})ln^{2}({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln(e^{x})ln^{3}({e^{x}}^{e^{x}}) + 18{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{3}(e^{x}) + 60{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{2}(e^{x}) + 55{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}(e^{x}) + 148{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln(e^{x}) + 7{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln^{2}({e^{x}}^{e^{x}}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln^{3}({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{8}}ln^{4}(e^{x}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{x}ln({e^{x}}^{e^{x}}) + 76{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{3}}ln({e^{x}}^{e^{x}}) + 4{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{8}}ln^{3}(e^{x}) + 15{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}}ln(e^{x}) + 54{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln({e^{x}}^{e^{x}}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{8}}ln^{2}(e^{x}) + 66{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln(e^{x}) + 36{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{2}({e^{x}}^{e^{x}}) + 4{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{5}}ln^{3}({e^{x}}^{e^{x}}) + 6{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}}ln^{2}({e^{x}}^{e^{x}}) + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}}ln^{4}({e^{x}}^{e^{x}}) + 4{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{7}}ln({e^{x}}^{e^{x}}) + 4{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{8}}ln(e^{x}) + 96{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{4}} + 32{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{2}} + 24{{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{6}} + {{e^{x}}^{e^{x}}}^{e^{x}}e^{{x}*{8}}\\ \end{split}\end{equation} \]