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

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