本次共计算 1 个题目:每一题对 x 求 2 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数sin(x){\frac{1}{cos(x)}}^{2} + \frac{ln(tan(\frac{x}{2} + \frac{pi}{4}))}{2} 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{sin(x)}{cos^{2}(x)} + \frac{1}{2}ln(tan(\frac{1}{2}x + \frac{1}{4}pi))\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{sin(x)}{cos^{2}(x)} + \frac{1}{2}ln(tan(\frac{1}{2}x + \frac{1}{4}pi))\right)}{dx}\\=&\frac{cos(x)}{cos^{2}(x)} + \frac{sin(x)*2sin(x)}{cos^{3}(x)} + \frac{\frac{1}{2}sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)(\frac{1}{2} + 0)}{(tan(\frac{1}{2}x + \frac{1}{4}pi))}\\=&\frac{1}{cos(x)} + \frac{2sin^{2}(x)}{cos^{3}(x)} + \frac{sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)}{4tan(\frac{1}{2}x + \frac{1}{4}pi)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{1}{cos(x)} + \frac{2sin^{2}(x)}{cos^{3}(x)} + \frac{sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)}{4tan(\frac{1}{2}x + \frac{1}{4}pi)}\right)}{dx}\\=&\frac{sin(x)}{cos^{2}(x)} + \frac{2*2sin(x)cos(x)}{cos^{3}(x)} + \frac{2sin^{2}(x)*3sin(x)}{cos^{4}(x)} + \frac{-sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)(\frac{1}{2} + 0)sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)}{4tan^{2}(\frac{1}{2}x + \frac{1}{4}pi)} + \frac{2sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)tan(\frac{1}{2}x + \frac{1}{4}pi)(\frac{1}{2} + 0)}{4tan(\frac{1}{2}x + \frac{1}{4}pi)}\\=&\frac{5sin(x)}{cos^{2}(x)} + \frac{6sin^{3}(x)}{cos^{4}(x)} - \frac{sec^{4}(\frac{1}{2}x + \frac{1}{4}pi)}{8tan^{2}(\frac{1}{2}x + \frac{1}{4}pi)} + \frac{sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)}{4}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!