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

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