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

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