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。\[ \begin{equation}\begin{split}【1/1】求函数{cos({cos(x)}^{2})}^{2} 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = cos^{2}(cos^{2}(x))\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( cos^{2}(cos^{2}(x))\right)}{dx}\\=&-2cos(cos^{2}(x))sin(cos^{2}(x))*-2cos(x)sin(x)\\=&4sin(x)sin(cos^{2}(x))cos(cos^{2}(x))cos(x)\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( 4sin(x)sin(cos^{2}(x))cos(cos^{2}(x))cos(x)\right)}{dx}\\=&4cos(x)sin(cos^{2}(x))cos(cos^{2}(x))cos(x) + 4sin(x)cos(cos^{2}(x))*-2cos(x)sin(x)cos(cos^{2}(x))cos(x) + 4sin(x)sin(cos^{2}(x))*-sin(cos^{2}(x))*-2cos(x)sin(x)cos(x) + 4sin(x)sin(cos^{2}(x))cos(cos^{2}(x))*-sin(x)\\=&4sin(cos^{2}(x))cos^{2}(x)cos(cos^{2}(x)) - 8sin^{2}(x)cos^{2}(cos^{2}(x))cos^{2}(x) + 8sin^{2}(cos^{2}(x))sin^{2}(x)cos^{2}(x) - 4sin^{2}(x)sin(cos^{2}(x))cos(cos^{2}(x))\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!