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

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