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

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