There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ -({e}^{x}) + {\frac{1}{x}}^{2} - (x + 1){e}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -2{e}^{x} - x{e}^{x} + \frac{1}{x^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -2{e}^{x} - x{e}^{x} + \frac{1}{x^{2}}\right)}{dx}\\=&-2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - {e}^{x} - x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + \frac{-2}{x^{3}}\\=&-3{e}^{x} - x{e}^{x} - \frac{2}{x^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -3{e}^{x} - x{e}^{x} - \frac{2}{x^{3}}\right)}{dx}\\=&-3({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - {e}^{x} - x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - \frac{2*-3}{x^{4}}\\=&-4{e}^{x} - x{e}^{x} + \frac{6}{x^{4}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -4{e}^{x} - x{e}^{x} + \frac{6}{x^{4}}\right)}{dx}\\=&-4({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - {e}^{x} - x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + \frac{6*-4}{x^{5}}\\=&-5{e}^{x} - x{e}^{x} - \frac{24}{x^{5}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -5{e}^{x} - x{e}^{x} - \frac{24}{x^{5}}\right)}{dx}\\=&-5({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - {e}^{x} - x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - \frac{24*-5}{x^{6}}\\=&-6{e}^{x} - x{e}^{x} + \frac{120}{x^{6}}\\ \end{split}\end{equation} \]

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