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

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