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

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