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

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