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

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