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

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