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

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