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

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