There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{(2 + 2x + xxx + 2e^{x})}{(xx)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2e^{x}}{x^{2}} + \frac{2}{x} + x + \frac{2}{x^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2e^{x}}{x^{2}} + \frac{2}{x} + x + \frac{2}{x^{2}}\right)}{dx}\\=&\frac{2*-2e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} + \frac{2*-1}{x^{2}} + 1 + \frac{2*-2}{x^{3}}\\=& - \frac{4e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} - \frac{2}{x^{2}} - \frac{4}{x^{3}} + 1\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{4e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} - \frac{2}{x^{2}} - \frac{4}{x^{3}} + 1\right)}{dx}\\=& - \frac{4*-3e^{x}}{x^{4}} - \frac{4e^{x}}{x^{3}} + \frac{2*-2e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} - \frac{2*-2}{x^{3}} - \frac{4*-3}{x^{4}} + 0\\=&\frac{12e^{x}}{x^{4}} - \frac{8e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} + \frac{4}{x^{3}} + \frac{12}{x^{4}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{12e^{x}}{x^{4}} - \frac{8e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} + \frac{4}{x^{3}} + \frac{12}{x^{4}}\right)}{dx}\\=&\frac{12*-4e^{x}}{x^{5}} + \frac{12e^{x}}{x^{4}} - \frac{8*-3e^{x}}{x^{4}} - \frac{8e^{x}}{x^{3}} + \frac{2*-2e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} + \frac{4*-3}{x^{4}} + \frac{12*-4}{x^{5}}\\=& - \frac{48e^{x}}{x^{5}} + \frac{36e^{x}}{x^{4}} - \frac{12e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} - \frac{12}{x^{4}} - \frac{48}{x^{5}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{48e^{x}}{x^{5}} + \frac{36e^{x}}{x^{4}} - \frac{12e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} - \frac{12}{x^{4}} - \frac{48}{x^{5}}\right)}{dx}\\=& - \frac{48*-5e^{x}}{x^{6}} - \frac{48e^{x}}{x^{5}} + \frac{36*-4e^{x}}{x^{5}} + \frac{36e^{x}}{x^{4}} - \frac{12*-3e^{x}}{x^{4}} - \frac{12e^{x}}{x^{3}} + \frac{2*-2e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} - \frac{12*-4}{x^{5}} - \frac{48*-5}{x^{6}}\\=&\frac{240e^{x}}{x^{6}} - \frac{192e^{x}}{x^{5}} + \frac{72e^{x}}{x^{4}} - \frac{16e^{x}}{x^{3}} + \frac{2e^{x}}{x^{2}} + \frac{48}{x^{5}} + \frac{240}{x^{6}}\\ \end{split}\end{equation} \]

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