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