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