There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ xe^{arctan(x)}{\frac{1}{(1 + {x}^{2})}}^{(\frac{3}{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{xe^{arctan(x)}}{(x^{2} + 1)^{\frac{3}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{xe^{arctan(x)}}{(x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 1)^{\frac{5}{2}}})xe^{arctan(x)} + \frac{e^{arctan(x)}}{(x^{2} + 1)^{\frac{3}{2}}} + \frac{xe^{arctan(x)}(\frac{(1)}{(1 + (x)^{2})})}{(x^{2} + 1)^{\frac{3}{2}}}\\=&\frac{-3x^{2}e^{arctan(x)}}{(x^{2} + 1)^{\frac{5}{2}}} + \frac{e^{arctan(x)}}{(x^{2} + 1)^{\frac{3}{2}}} + \frac{xe^{arctan(x)}}{(x^{2} + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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