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

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