There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ x - \frac{(2x - {e}^{x} + 3)}{(2 - {e}^{x})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x - \frac{2x}{(-{e}^{x} + 2)} + \frac{{e}^{x}}{(-{e}^{x} + 2)} - \frac{3}{(-{e}^{x} + 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x - \frac{2x}{(-{e}^{x} + 2)} + \frac{{e}^{x}}{(-{e}^{x} + 2)} - \frac{3}{(-{e}^{x} + 2)}\right)}{dx}\\=&1 - 2(\frac{-(-({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 0)}{(-{e}^{x} + 2)^{2}})x - \frac{2}{(-{e}^{x} + 2)} + (\frac{-(-({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 0)}{(-{e}^{x} + 2)^{2}}){e}^{x} + \frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{(-{e}^{x} + 2)} - 3(\frac{-(-({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 0)}{(-{e}^{x} + 2)^{2}})\\=&\frac{{e}^{x}}{(-{e}^{x} + 2)} + \frac{{e}^{(2x)}}{(-{e}^{x} + 2)^{2}} - \frac{2x{e}^{x}}{(-{e}^{x} + 2)^{2}} - \frac{3{e}^{x}}{(-{e}^{x} + 2)^{2}} - \frac{2}{(-{e}^{x} + 2)} + 1\\ \end{split}\end{equation} \]

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