本次共计算 1 个题目:每一题对 x 求 4 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数cos(sin(x)) - cos(x) 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( cos(sin(x)) - cos(x)\right)}{dx}\\=&-sin(sin(x))cos(x) - -sin(x)\\=&-sin(sin(x))cos(x) + sin(x)\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( -sin(sin(x))cos(x) + sin(x)\right)}{dx}\\=&-cos(sin(x))cos(x)cos(x) - sin(sin(x))*-sin(x) + cos(x)\\=&-cos^{2}(x)cos(sin(x)) + sin(x)sin(sin(x)) + cos(x)\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( -cos^{2}(x)cos(sin(x)) + sin(x)sin(sin(x)) + cos(x)\right)}{dx}\\=&--2cos(x)sin(x)cos(sin(x)) - cos^{2}(x)*-sin(sin(x))cos(x) + cos(x)sin(sin(x)) + sin(x)cos(sin(x))cos(x) + -sin(x)\\=&3sin(x)cos(x)cos(sin(x)) + sin(sin(x))cos^{3}(x) + sin(sin(x))cos(x) - sin(x)\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( 3sin(x)cos(x)cos(sin(x)) + sin(sin(x))cos^{3}(x) + sin(sin(x))cos(x) - sin(x)\right)}{dx}\\=&3cos(x)cos(x)cos(sin(x)) + 3sin(x)*-sin(x)cos(sin(x)) + 3sin(x)cos(x)*-sin(sin(x))cos(x) + cos(sin(x))cos(x)cos^{3}(x) + sin(sin(x))*-3cos^{2}(x)sin(x) + cos(sin(x))cos(x)cos(x) + sin(sin(x))*-sin(x) - cos(x)\\=&4cos^{2}(x)cos(sin(x)) - 3sin^{2}(x)cos(sin(x)) - 6sin(x)sin(sin(x))cos^{2}(x) + cos^{4}(x)cos(sin(x)) - sin(x)sin(sin(x)) - cos(x)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!