本次共计算 1 个题目：每一题对 x 求 3 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数cos(\frac{{x}^{2}}{k}) 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = cos(\frac{x^{2}}{k})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos(\frac{x^{2}}{k})\right)}{dx}\\=&\frac{-sin(\frac{x^{2}}{k})*2x}{k}\\=&\frac{-2xsin(\frac{x^{2}}{k})}{k}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-2xsin(\frac{x^{2}}{k})}{k}\right)}{dx}\\=&\frac{-2sin(\frac{x^{2}}{k})}{k} - \frac{2xcos(\frac{x^{2}}{k})*2x}{kk}\\=&\frac{-2sin(\frac{x^{2}}{k})}{k} - \frac{4x^{2}cos(\frac{x^{2}}{k})}{k^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2sin(\frac{x^{2}}{k})}{k} - \frac{4x^{2}cos(\frac{x^{2}}{k})}{k^{2}}\right)}{dx}\\=&\frac{-2cos(\frac{x^{2}}{k})*2x}{kk} - \frac{4*2xcos(\frac{x^{2}}{k})}{k^{2}} - \frac{4x^{2}*-sin(\frac{x^{2}}{k})*2x}{k^{2}k}\\=&\frac{-12xcos(\frac{x^{2}}{k})}{k^{2}} + \frac{8x^{3}sin(\frac{x^{2}}{k})}{k^{3}}\\ \end{split}\end{equation} \]

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