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

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