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

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