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。
\[ \begin{equation}\begin{split}【1/1】求函数{(x + {(x + {(x)}^{\frac{1}{6}})}^{\frac{1}{6}})}^{\frac{1}{6}} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (x + (x + x^{\frac{1}{6}})^{\frac{1}{6}})^{\frac{1}{6}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( (x + (x + x^{\frac{1}{6}})^{\frac{1}{6}})^{\frac{1}{6}}\right)}{dx}\\=&(\frac{\frac{1}{6}(1 + (\frac{\frac{1}{6}(1 + \frac{\frac{1}{6}}{x^{\frac{5}{6}}})}{(x + x^{\frac{1}{6}})^{\frac{5}{6}}}))}{(x + (x + x^{\frac{1}{6}})^{\frac{1}{6}})^{\frac{5}{6}}})\\=&\frac{1}{216(x + x^{\frac{1}{6}})^{\frac{5}{6}}(x + (x + x^{\frac{1}{6}})^{\frac{1}{6}})^{\frac{5}{6}}x^{\frac{5}{6}}} + \frac{1}{36(x + x^{\frac{1}{6}})^{\frac{5}{6}}(x + (x + x^{\frac{1}{6}})^{\frac{1}{6}})^{\frac{5}{6}}} + \frac{1}{6(x + (x + x^{\frac{1}{6}})^{\frac{1}{6}})^{\frac{5}{6}}}\\ \end{split}\end{equation} \]

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！