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

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