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

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