There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {{2}^{{({{{e}^{x}}^{x}}^{{e}^{x}})}^{{e}^{x}}}}^{({e}^{5}x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {{2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}}^{(xe^{5})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}}^{(xe^{5})}\right)}{dx}\\=&({{2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}}^{(xe^{5})}((e^{5} + x*5e^{4}*0)ln({2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}) + \frac{(xe^{5})(({2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}((({{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}((({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))ln({{{e}^{x}}^{x}}^{{e}^{x}}) + \frac{({e}^{x})(({{{e}^{x}}^{x}}^{{e}^{x}}((({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))ln({{e}^{x}}^{x}) + \frac{({e}^{x})(({{e}^{x}}^{x}((1)ln({e}^{x}) + \frac{(x)(({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))}{({e}^{x})})))}{({{e}^{x}}^{x})})))}{({{{e}^{x}}^{x}}^{{e}^{x}})})))ln(2) + \frac{({{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}})(0)}{(2)})))}{({2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}})}))\\=&{{2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}}^{(xe^{5})}e^{5}ln({2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}) + x{e}^{x}{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}{{2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}}^{(xe^{5})}e^{5}ln(2)ln({{{e}^{x}}^{x}}^{{e}^{x}}) + x{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}{e}^{(2x)}{{2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}}^{(xe^{5})}e^{5}ln(2)ln({{e}^{x}}^{x}) + x{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}{e}^{(2x)}{{2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}}^{(xe^{5})}e^{5}ln(2)ln({e}^{x}) + x^{2}{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}{{2}^{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}}^{(xe^{5})}e^{5}ln(2)\\ \end{split}\end{equation} \]

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