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

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