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

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