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

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