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

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