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

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