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。\[ \begin{equation}\begin{split}【1/1】求函数arccos(x{({x}^{2} + {y}^{2})}^{\frac{-1}{2}}) 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arccos(\frac{x}{(x^{2} + y^{2})^{\frac{1}{2}}})\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( arccos(\frac{x}{(x^{2} + y^{2})^{\frac{1}{2}}})\right)}{dx}\\=&(\frac{-((\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{3}{2}}})x + \frac{1}{(x^{2} + y^{2})^{\frac{1}{2}}})}{((1 - (\frac{x}{(x^{2} + y^{2})^{\frac{1}{2}}})^{2})^{\frac{1}{2}})})\\=&\frac{x^{2}}{(\frac{-x^{2}}{(x^{2} + y^{2})} + 1)^{\frac{1}{2}}(x^{2} + y^{2})^{\frac{3}{2}}} - \frac{1}{(\frac{-x^{2}}{(x^{2} + y^{2})} + 1)^{\frac{1}{2}}(x^{2} + y^{2})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!