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。\[ \begin{equation}\begin{split}【1/1】求函数tan(sin(x)) 关于 x 的 3 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( tan(sin(x))\right)}{dx}\\=&sec^{2}(sin(x))(cos(x))\\=&cos(x)sec^{2}(sin(x))\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( cos(x)sec^{2}(sin(x))\right)}{dx}\\=&-sin(x)sec^{2}(sin(x)) + cos(x)*2sec^{2}(sin(x))tan(sin(x))cos(x)\\=&-sin(x)sec^{2}(sin(x)) + 2cos^{2}(x)tan(sin(x))sec^{2}(sin(x))\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( -sin(x)sec^{2}(sin(x)) + 2cos^{2}(x)tan(sin(x))sec^{2}(sin(x))\right)}{dx}\\=&-cos(x)sec^{2}(sin(x)) - sin(x)*2sec^{2}(sin(x))tan(sin(x))cos(x) + 2*-2cos(x)sin(x)tan(sin(x))sec^{2}(sin(x)) + 2cos^{2}(x)sec^{2}(sin(x))(cos(x))sec^{2}(sin(x)) + 2cos^{2}(x)tan(sin(x))*2sec^{2}(sin(x))tan(sin(x))cos(x)\\=&-cos(x)sec^{2}(sin(x)) - 6sin(x)cos(x)tan(sin(x))sec^{2}(sin(x)) + 2cos^{3}(x)sec^{4}(sin(x)) + 4cos^{3}(x)tan^{2}(sin(x))sec^{2}(sin(x))\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!