本次共计算 1 个题目:每一题对 x 求 3 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数2x{cos(x)}^{2} - 2cos(x)sin(x) 关于 x 的 3 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 2xcos^{2}(x) - 2sin(x)cos(x)\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( 2xcos^{2}(x) - 2sin(x)cos(x)\right)}{dx}\\=&2cos^{2}(x) + 2x*-2cos(x)sin(x) - 2cos(x)cos(x) - 2sin(x)*-sin(x)\\=&-4xsin(x)cos(x) + 2sin^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( -4xsin(x)cos(x) + 2sin^{2}(x)\right)}{dx}\\=&-4sin(x)cos(x) - 4xcos(x)cos(x) - 4xsin(x)*-sin(x) + 2*2sin(x)cos(x)\\=& - 4xcos^{2}(x) + 4xsin^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( - 4xcos^{2}(x) + 4xsin^{2}(x)\right)}{dx}\\=& - 4cos^{2}(x) - 4x*-2cos(x)sin(x) + 4sin^{2}(x) + 4x*2sin(x)cos(x)\\=& - 4cos^{2}(x) + 16xsin(x)cos(x) + 4sin^{2}(x)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!