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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{(x + 1)sqrt(x - 1)}{sqrt(sqrt(x + 2))} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{xsqrt(x - 1)}{sqrt(sqrt(x + 2))} + \frac{sqrt(x - 1)}{sqrt(sqrt(x + 2))}\right)}{dx}\\=&\frac{sqrt(x - 1)}{sqrt(sqrt(x + 2))} + \frac{x(1 + 0)*\frac{1}{2}}{(x - 1)^{\frac{1}{2}}sqrt(sqrt(x + 2))} + \frac{xsqrt(x - 1)*-(1 + 0)*\frac{1}{2}*\frac{1}{2}}{(sqrt(x + 2))(x + 2)^{\frac{1}{2}}(sqrt(x + 2))^{\frac{1}{2}}} + \frac{(1 + 0)*\frac{1}{2}}{(x - 1)^{\frac{1}{2}}sqrt(sqrt(x + 2))} + \frac{sqrt(x - 1)*-(1 + 0)*\frac{1}{2}*\frac{1}{2}}{(sqrt(x + 2))(x + 2)^{\frac{1}{2}}(sqrt(x + 2))^{\frac{1}{2}}}\\=&\frac{sqrt(x - 1)}{sqrt(sqrt(x + 2))} + \frac{x}{2(x - 1)^{\frac{1}{2}}sqrt(sqrt(x + 2))} - \frac{xsqrt(x - 1)}{4(x + 2)^{\frac{1}{2}}sqrt(x + 2)^{\frac{3}{2}}} + \frac{1}{2(x - 1)^{\frac{1}{2}}sqrt(sqrt(x + 2))} - \frac{sqrt(x - 1)}{4(x + 2)^{\frac{1}{2}}sqrt(x + 2)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!