There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (-{\frac{1}{(x - 1)}}^{2})(ln(x) - \frac{2(x - 1)}{(x + 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-ln(x)}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}(x + 1)} - \frac{2}{(x - 1)^{2}(x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-ln(x)}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}(x + 1)} - \frac{2}{(x - 1)^{2}(x + 1)}\right)}{dx}\\=&-(\frac{-2(1 + 0)}{(x - 1)^{3}})ln(x) - \frac{1}{(x - 1)^{2}(x)} + \frac{2(\frac{-2(1 + 0)}{(x - 1)^{3}})x}{(x + 1)} + \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})x}{(x - 1)^{2}} + \frac{2}{(x - 1)^{2}(x + 1)} - \frac{2(\frac{-2(1 + 0)}{(x - 1)^{3}})}{(x + 1)} - \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})}{(x - 1)^{2}}\\=&\frac{2ln(x)}{(x - 1)^{3}} - \frac{1}{(x - 1)^{2}x} - \frac{4x}{(x - 1)^{3}(x + 1)} - \frac{2x}{(x + 1)^{2}(x - 1)^{2}} + \frac{4}{(x - 1)^{3}(x + 1)} + \frac{2}{(x + 1)^{2}(x - 1)^{2}} + \frac{2}{(x - 1)^{2}(x + 1)}\\ \end{split}\end{equation} \]

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