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。\[ \begin{equation}\begin{split}【1/1】求函数{(sin(x))}^{2}ln(x) 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = ln(x)sin^{2}(x)\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( ln(x)sin^{2}(x)\right)}{dx}\\=&\frac{sin^{2}(x)}{(x)} + ln(x)*2sin(x)cos(x)\\=&\frac{sin^{2}(x)}{x} + 2ln(x)sin(x)cos(x)\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{sin^{2}(x)}{x} + 2ln(x)sin(x)cos(x)\right)}{dx}\\=&\frac{-sin^{2}(x)}{x^{2}} + \frac{2sin(x)cos(x)}{x} + \frac{2sin(x)cos(x)}{(x)} + 2ln(x)cos(x)cos(x) + 2ln(x)sin(x)*-sin(x)\\=&\frac{4sin(x)cos(x)}{x} - \frac{sin^{2}(x)}{x^{2}} + 2ln(x)cos^{2}(x) - 2ln(x)sin^{2}(x)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!