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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{-x{(sec(\frac{x}{y}))}^{2}}{({y}^{2}tan(\frac{x}{y}))} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{-xsec^{2}(\frac{x}{y})}{y^{2}tan(\frac{x}{y})}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{-xsec^{2}(\frac{x}{y})}{y^{2}tan(\frac{x}{y})}\right)}{dx}\\=&\frac{-sec^{2}(\frac{x}{y})}{y^{2}tan(\frac{x}{y})} - \frac{x*-sec^{2}(\frac{x}{y})(\frac{1}{y})sec^{2}(\frac{x}{y})}{y^{2}tan^{2}(\frac{x}{y})} - \frac{x*2sec^{2}(\frac{x}{y})tan(\frac{x}{y})}{y^{2}tan(\frac{x}{y})y}\\=&\frac{-sec^{2}(\frac{x}{y})}{y^{2}tan(\frac{x}{y})} + \frac{xsec^{4}(\frac{x}{y})}{y^{3}tan^{2}(\frac{x}{y})} - \frac{2xsec^{2}(\frac{x}{y})}{y^{3}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!