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。\[ \begin{equation}\begin{split}【1/1】求函数{((x + \frac{(x + 1){(\frac{(8a - 1)}{3})}^{\frac{1}{2}}}{3}))}^{\frac{1}{3}} + {((x - \frac{(x + 1){(\frac{(8a - 1)}{3})}^{\frac{1}{2}}}{3}))}^{\frac{1}{3}} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{1}{3}} + (x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{1}{3}}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( (x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{1}{3}} + (x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{1}{3}}\right)}{dx}\\=&(\frac{\frac{1}{3}(1 + \frac{1}{3}(\frac{\frac{1}{2}(0 + 0)}{(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}})x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}} + \frac{1}{3}(\frac{\frac{1}{2}(0 + 0)}{(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}}))}{(x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{2}{3}}}) + (\frac{\frac{1}{3}(1 - \frac{1}{3}(\frac{\frac{1}{2}(0 + 0)}{(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}})x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}} - \frac{1}{3}(\frac{\frac{1}{2}(0 + 0)}{(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}}))}{(x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{2}{3}}})\\=&\frac{(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}}{9(x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{2}{3}}} - \frac{(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}}{9(x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{2}{3}}} + \frac{1}{3(x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x + \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{2}{3}}} + \frac{1}{3(x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}}x - \frac{1}{3}(\frac{8}{3}a - \frac{1}{3})^{\frac{1}{2}})^{\frac{2}{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!