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

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