There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {e}^{(xxxxxxxx)}{{({{{e}^{x}}^{x}}^{{e}^{x}})}^{{e}^{x}}}^{({e}^{5}x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{x^{8}}{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{x^{8}}{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})}\right)}{dx}\\=&({e}^{x^{8}}((8x^{7})ln(e) + \frac{(x^{8})(0)}{(e)})){{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})} + {e}^{x^{8}}({{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})}((e^{5} + x*5e^{4}*0)ln({{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}) + \frac{(xe^{5})(({{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}((({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))ln({{{e}^{x}}^{x}}^{{e}^{x}}) + \frac{({e}^{x})(({{{e}^{x}}^{x}}^{{e}^{x}}((({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))ln({{e}^{x}}^{x}) + \frac{({e}^{x})(({{e}^{x}}^{x}((1)ln({e}^{x}) + \frac{(x)(({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))}{({e}^{x})})))}{({{e}^{x}}^{x})})))}{({{{e}^{x}}^{x}}^{{e}^{x}})})))}{({{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}})}))\\=&x{e}^{(2x)}{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})}e^{5}ln({{{e}^{x}}^{x}}^{{e}^{x}}) + {{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})}{e}^{x^{8}}e^{5}ln({{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}) + x{e}^{(4x)}{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})}e^{5}ln({{e}^{x}}^{x}) + x{e}^{(4x)}{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})}e^{5}ln({e}^{x}) + x^{2}{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})}{e}^{x^{8}}e^{5} + 8x^{7}{e}^{x^{8}}{{{{{e}^{x}}^{x}}^{{e}^{x}}}^{{e}^{x}}}^{(xe^{5})}\\ \end{split}\end{equation} \]

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