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

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