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

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