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

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