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

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