There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{(x - {e}^{-1})}^{2}}{({e}^{x})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{2x{e}^{(-x)}}{e} + x^{2}{e}^{(-x)} + \frac{{e}^{(-x)}}{e^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{2x{e}^{(-x)}}{e} + x^{2}{e}^{(-x)} + \frac{{e}^{(-x)}}{e^{2}}\right)}{dx}\\=& - \frac{2{e}^{(-x)}}{e} - \frac{2x({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)}))}{e} - \frac{2x{e}^{(-x)}*-0}{e^{2}} + 2x{e}^{(-x)} + x^{2}({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)})) + \frac{({e}^{(-x)}((-1)ln(e) + \frac{(-x)(0)}{(e)}))}{e^{2}} + \frac{{e}^{(-x)}*-2*0}{e^{3}}\\=& - \frac{2{e}^{(-x)}}{e} + \frac{2x{e}^{(-x)}}{e} + 2x{e}^{(-x)} - x^{2}{e}^{(-x)} - \frac{{e}^{(-x)}}{e^{2}}\\ \end{split}\end{equation} \]

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