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

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