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