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

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