本次共计算 1 个题目：每一题对 x 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{xy({x}^{2} - {y}^{2})}{({x}^{2} + {y}^{2})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{yx^{3}}{(x^{2} + y^{2})} - \frac{y^{3}x}{(x^{2} + y^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{yx^{3}}{(x^{2} + y^{2})} - \frac{y^{3}x}{(x^{2} + y^{2})}\right)}{dx}\\=&(\frac{-(2x + 0)}{(x^{2} + y^{2})^{2}})yx^{3} + \frac{y*3x^{2}}{(x^{2} + y^{2})} - (\frac{-(2x + 0)}{(x^{2} + y^{2})^{2}})y^{3}x - \frac{y^{3}}{(x^{2} + y^{2})}\\=&\frac{-2yx^{4}}{(x^{2} + y^{2})^{2}} + \frac{3yx^{2}}{(x^{2} + y^{2})} + \frac{2y^{3}x^{2}}{(x^{2} + y^{2})^{2}} - \frac{y^{3}}{(x^{2} + y^{2})}\\ \end{split}\end{equation} \]

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