There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{e}^{x}}{(2sin(4x + 7))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{1}{2}{e}^{x}}{sin(4x + 7)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{1}{2}{e}^{x}}{sin(4x + 7)}\right)}{dx}\\=&\frac{\frac{1}{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{sin(4x + 7)} + \frac{\frac{1}{2}{e}^{x}*-cos(4x + 7)(4 + 0)}{sin^{2}(4x + 7)}\\=&\frac{-2{e}^{x}cos(4x + 7)}{sin^{2}(4x + 7)} + \frac{{e}^{x}}{2sin(4x + 7)}\\ \end{split}\end{equation} \]

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