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





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