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

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