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。\[ \begin{equation}\begin{split}【1/1】求函数4sin(x) - 4cos(x) + xcos(x) + xsin(x) 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( 4sin(x) - 4cos(x) + xcos(x) + xsin(x)\right)}{dx}\\=&4cos(x) - 4*-sin(x) + cos(x) + x*-sin(x) + sin(x) + xcos(x)\\=&5cos(x) + 5sin(x) - xsin(x) + xcos(x)\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( 5cos(x) + 5sin(x) - xsin(x) + xcos(x)\right)}{dx}\\=&5*-sin(x) + 5cos(x) - sin(x) - xcos(x) + cos(x) + x*-sin(x)\\=&-6sin(x) + 6cos(x) - xcos(x) - xsin(x)\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( -6sin(x) + 6cos(x) - xcos(x) - xsin(x)\right)}{dx}\\=&-6cos(x) + 6*-sin(x) - cos(x) - x*-sin(x) - sin(x) - xcos(x)\\=&-7cos(x) - 7sin(x) + xsin(x) - xcos(x)\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( -7cos(x) - 7sin(x) + xsin(x) - xcos(x)\right)}{dx}\\=&-7*-sin(x) - 7cos(x) + sin(x) + xcos(x) - cos(x) - x*-sin(x)\\=&8sin(x) - 8cos(x) + xcos(x) + xsin(x)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!