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

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