There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-arctan(x){\frac{1}{(1 + {x}^{2})}}^{3}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{-1}{2}arctan(x)}{(x^{2} + 1)^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{-1}{2}arctan(x)}{(x^{2} + 1)^{3}}\right)}{dx}\\=&\frac{-1}{2}(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})arctan(x) - \frac{\frac{1}{2}(\frac{(1)}{(1 + (x)^{2})})}{(x^{2} + 1)^{3}}\\=&\frac{3xarctan(x)}{(x^{2} + 1)^{4}} - \frac{1}{2(x^{2} + 1)^{4}}\\ \end{split}\end{equation} \]

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