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

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