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 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {e}^{x}(x - 1){\frac{1}{x}}^{2}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{e}^{x}}{x} - \frac{{e}^{x}}{x^{2}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{{e}^{x}}{x} - \frac{{e}^{x}}{x^{2}}\right)}{dx}\\=&\frac{-{e}^{x}}{x^{2}} + \frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{x} - \frac{-2{e}^{x}}{x^{3}} - \frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{x^{2}}\\=&\frac{-2{e}^{x}}{x^{2}} + \frac{{e}^{x}}{x} + \frac{2{e}^{x}}{x^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2{e}^{x}}{x^{2}} + \frac{{e}^{x}}{x} + \frac{2{e}^{x}}{x^{3}}\right)}{dx}\\=&\frac{-2*-2{e}^{x}}{x^{3}} - \frac{2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{x^{2}} + \frac{-{e}^{x}}{x^{2}} + \frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{x} + \frac{2*-3{e}^{x}}{x^{4}} + \frac{2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{x^{3}}\\=&\frac{6{e}^{x}}{x^{3}} - \frac{3{e}^{x}}{x^{2}} + \frac{{e}^{x}}{x} - \frac{6{e}^{x}}{x^{4}}\\ \end{split}\end{equation} \]





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