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。\[ \begin{equation}\begin{split}【1/1】求函数(1 - cos(x))(x - sin(x)) 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - xcos(x) + sin(x)cos(x) + x - sin(x)\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( - xcos(x) + sin(x)cos(x) + x - sin(x)\right)}{dx}\\=& - cos(x) - x*-sin(x) + cos(x)cos(x) + sin(x)*-sin(x) + 1 - cos(x)\\=& - 2cos(x) + xsin(x) + cos^{2}(x) - sin^{2}(x) + 1\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( - 2cos(x) + xsin(x) + cos^{2}(x) - sin^{2}(x) + 1\right)}{dx}\\=& - 2*-sin(x) + sin(x) + xcos(x) + -2cos(x)sin(x) - 2sin(x)cos(x) + 0\\=& - 4sin(x)cos(x) + 3sin(x) + xcos(x)\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( - 4sin(x)cos(x) + 3sin(x) + xcos(x)\right)}{dx}\\=& - 4cos(x)cos(x) - 4sin(x)*-sin(x) + 3cos(x) + cos(x) + x*-sin(x)\\=& - 4cos^{2}(x) + 4sin^{2}(x) + 4cos(x) - xsin(x)\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( - 4cos^{2}(x) + 4sin^{2}(x) + 4cos(x) - xsin(x)\right)}{dx}\\=& - 4*-2cos(x)sin(x) + 4*2sin(x)cos(x) + 4*-sin(x) - sin(x) - xcos(x)\\=&16sin(x)cos(x) - 5sin(x) - xcos(x)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!