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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(2({z}^{2}) - {x}^{2} - {y}^{2})}{({(sqrt({x}^{2} + {y}^{2} + {z}^{2}))}^{4})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{2z^{2}}{sqrt(x^{2} + y^{2} + z^{2})^{4}} - \frac{x^{2}}{sqrt(x^{2} + y^{2} + z^{2})^{4}} - \frac{y^{2}}{sqrt(x^{2} + y^{2} + z^{2})^{4}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{2z^{2}}{sqrt(x^{2} + y^{2} + z^{2})^{4}} - \frac{x^{2}}{sqrt(x^{2} + y^{2} + z^{2})^{4}} - \frac{y^{2}}{sqrt(x^{2} + y^{2} + z^{2})^{4}}\right)}{dx}\\=&\frac{2z^{2}*-4(2x + 0 + 0)*\frac{1}{2}}{(x^{2} + y^{2} + z^{2})^{\frac{5}{2}}(x^{2} + y^{2} + z^{2})^{\frac{1}{2}}} - \frac{2x}{sqrt(x^{2} + y^{2} + z^{2})^{4}} - \frac{x^{2}*-4(2x + 0 + 0)*\frac{1}{2}}{(x^{2} + y^{2} + z^{2})^{\frac{5}{2}}(x^{2} + y^{2} + z^{2})^{\frac{1}{2}}} - \frac{y^{2}*-4(2x + 0 + 0)*\frac{1}{2}}{(x^{2} + y^{2} + z^{2})^{\frac{5}{2}}(x^{2} + y^{2} + z^{2})^{\frac{1}{2}}}\\=&\frac{-8z^{2}x}{(x^{2} + y^{2} + z^{2})^{3}} - \frac{2x}{sqrt(x^{2} + y^{2} + z^{2})^{4}} + \frac{4x^{3}}{(x^{2} + y^{2} + z^{2})^{3}} + \frac{4y^{2}x}{(x^{2} + y^{2} + z^{2})^{3}}\\ \end{split}\end{equation} \]

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