There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {{{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}}^{tan(e^{x})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}}^{tan(e^{x})}\right)}{dx}\\=&({{{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}}^{tan(e^{x})}((sec^{2}(e^{x})(e^{x}))ln({{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}) + \frac{(tan(e^{x}))(({{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}((e^{e^{x}}e^{x})ln({{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}) + \frac{(e^{e^{x}})(({{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}((-sin({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln({{x}^{ln(x)}}^{sin(x)}) + \frac{(cos({x}^{x}))(({{x}^{ln(x)}}^{sin(x)}((cos(x))ln({x}^{ln(x)}) + \frac{(sin(x))(({x}^{ln(x)}((\frac{1}{(x)})ln(x) + \frac{(ln(x))(1)}{(x)})))}{({x}^{ln(x)})})))}{({{x}^{ln(x)}}^{sin(x)})})))}{({{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})})})))}{({{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}})}))\\=&{{{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}}^{tan(e^{x})}e^{x}ln({{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}})sec^{2}(e^{x}) + {{{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}}^{tan(e^{x})}e^{e^{x}}e^{x}ln({{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})})tan(e^{x}) - {x}^{x}{{{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}}^{tan(e^{x})}e^{e^{x}}ln(x)ln({{x}^{ln(x)}}^{sin(x)})sin({x}^{x})tan(e^{x}) - {x}^{x}{{{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}}^{tan(e^{x})}e^{e^{x}}ln({{x}^{ln(x)}}^{sin(x)})sin({x}^{x})tan(e^{x}) + {{{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}}^{tan(e^{x})}e^{e^{x}}ln({x}^{ln(x)})cos(x)cos({x}^{x})tan(e^{x}) + \frac{2{{{{{x}^{ln(x)}}^{sin(x)}}^{cos({x}^{x})}}^{e^{e^{x}}}}^{tan(e^{x})}e^{e^{x}}ln(x)sin(x)cos({x}^{x})tan(e^{x})}{x}\\ \end{split}\end{equation} \]

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