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

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