There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {e}^{x} - \frac{1}{10}{e}^{x}cos(2x) - \frac{1}{5}{e}^{x}sin(2x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{1}{10}{e}^{x}cos(2x) - \frac{1}{5}{e}^{x}sin(2x) + {e}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{1}{10}{e}^{x}cos(2x) - \frac{1}{5}{e}^{x}sin(2x) + {e}^{x}\right)}{dx}\\=& - \frac{1}{10}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x) - \frac{1}{10}{e}^{x}*-sin(2x)*2 - \frac{1}{5}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x) - \frac{1}{5}{e}^{x}cos(2x)*2 + ({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=& - \frac{{e}^{x}cos(2x)}{2} + {e}^{x}\\ \end{split}\end{equation} \]

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