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。\[ \begin{equation}\begin{split}【1/1】求函数{x}^{(\frac{2}{3})} + \frac{e{(pi - {x}^{2})}^{\frac{1}{2}}sin(8pix)}{3} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{1}{3}(pi - x^{2})^{\frac{1}{2}}esin(8pix) + x^{\frac{2}{3}}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{1}{3}(pi - x^{2})^{\frac{1}{2}}esin(8pix) + x^{\frac{2}{3}}\right)}{dx}\\=&\frac{1}{3}(\frac{\frac{1}{2}(0 - 2x)}{(pi - x^{2})^{\frac{1}{2}}})esin(8pix) + \frac{1}{3}(pi - x^{2})^{\frac{1}{2}}*0sin(8pix) + \frac{1}{3}(pi - x^{2})^{\frac{1}{2}}ecos(8pix)*8pi + \frac{\frac{2}{3}}{x^{\frac{1}{3}}}\\=& - \frac{xesin(8pix)}{3(pi - x^{2})^{\frac{1}{2}}} + \frac{8(pi - x^{2})^{\frac{1}{2}}piecos(8pix)}{3} + \frac{2}{3x^{\frac{1}{3}}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!