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