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

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