神马作文网求(cos x)^3的n阶导数
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/12 11:40:25
求(cos x)^3的n阶导数
用Matlab做的,8解导数的结果如下,找找规律,可用数学归纳法证明.
-3*cos(x)^2*sin(x),
6*cos(x)*sin(x)^2-3*cos(x)^3,
-6*sin(x)^3+21*cos(x)^2*sin(x),
-60*cos(x)*sin(x)^2+21*cos(x)^3,
60*sin(x)^3-183*cos(x)^2*sin(x),
546*cos(x)*sin(x)^2-183*cos(x)^3,
-546*sin(x)^3+1641*cos(x)^2*sin(x),
-4920*cos(x)*sin(x)^2+1641*cos(x)^3
-3*cos(x)^2*sin(x),
6*cos(x)*sin(x)^2-3*cos(x)^3,
-6*sin(x)^3+21*cos(x)^2*sin(x),
-60*cos(x)*sin(x)^2+21*cos(x)^3,
60*sin(x)^3-183*cos(x)^2*sin(x),
546*cos(x)*sin(x)^2-183*cos(x)^3,
-546*sin(x)^3+1641*cos(x)^2*sin(x),
-4920*cos(x)*sin(x)^2+1641*cos(x)^3