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

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