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

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