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

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