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

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