There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (2{\frac{1}{e}}^{(x + π)} - 1)sin(x + \frac{3π}{2}) - 3\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2{\frac{1}{e}}^{(x + π)}sin(x + \frac{3}{2}π) - sin(x + \frac{3}{2}π) - 3\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2{\frac{1}{e}}^{(x + π)}sin(x + \frac{3}{2}π) - sin(x + \frac{3}{2}π) - 3\right)}{dx}\\=&2({\frac{1}{e}}^{(x + π)}((1 + 0)ln(\frac{1}{e}) + \frac{(x + π)(\frac{-0}{e^{2}})}{(\frac{1}{e})}))sin(x + \frac{3}{2}π) + 2{\frac{1}{e}}^{(x + π)}cos(x + \frac{3}{2}π)(1 + 0) - cos(x + \frac{3}{2}π)(1 + 0) + 0\\=&-2{\frac{1}{e}}^{(x + π)}sin(x + \frac{3}{2}π) + 2{\frac{1}{e}}^{(x + π)}cos(x + \frac{3}{2}π) - cos(x + \frac{3}{2}π)\\ \end{split}\end{equation} \]

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