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

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