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

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！