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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{(1 - {(1 - \frac{x}{w})}^{\frac{1}{2}})}{(1 - {(1 - \frac{y}{w})}^{\frac{1}{2}})} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - \frac{(\frac{-x}{w} + 1)^{\frac{1}{2}}}{(-(\frac{-y}{w} + 1)^{\frac{1}{2}} + 1)} + \frac{1}{(-(\frac{-y}{w} + 1)^{\frac{1}{2}} + 1)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( - \frac{(\frac{-x}{w} + 1)^{\frac{1}{2}}}{(-(\frac{-y}{w} + 1)^{\frac{1}{2}} + 1)} + \frac{1}{(-(\frac{-y}{w} + 1)^{\frac{1}{2}} + 1)}\right)}{dx}\\=& - (\frac{-(-(\frac{\frac{1}{2}(0 + 0)}{(\frac{-y}{w} + 1)^{\frac{1}{2}}}) + 0)}{(-(\frac{-y}{w} + 1)^{\frac{1}{2}} + 1)^{2}})(\frac{-x}{w} + 1)^{\frac{1}{2}} - \frac{(\frac{\frac{1}{2}(\frac{-1}{w} + 0)}{(\frac{-x}{w} + 1)^{\frac{1}{2}}})}{(-(\frac{-y}{w} + 1)^{\frac{1}{2}} + 1)} + (\frac{-(-(\frac{\frac{1}{2}(0 + 0)}{(\frac{-y}{w} + 1)^{\frac{1}{2}}}) + 0)}{(-(\frac{-y}{w} + 1)^{\frac{1}{2}} + 1)^{2}})\\=&\frac{1}{2(\frac{-x}{w} + 1)^{\frac{1}{2}}(-(\frac{-y}{w} + 1)^{\frac{1}{2}} + 1)w}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!