Question

大一高数，求n阶导，麻烦写一下解题过程

Answer 1

首先,利用两次积化和差公式:
sinXsin2Xsin3X
=-(1/2)(cos3X-cosX)sin3X
=-1/4(sin6X)+1/2(sin4X)+1/2sin(2X)

分别设u1,u2,u3为-1/4(sin6X),1/2(sin4X),1/2sin(2X)
则u1的n阶导数为-1/4(sin(6X+n(π/2))*6^(n).
这个是复合函数求导
同理u2的n阶导数为1/2(sin(4X+n(π/2))*4^(n)
u3的n阶导数为1/2(sin(2X+n(π/2))*2^(n)
最后y的n阶导数
=u1的n阶导数+u2的n阶导数+u3的n阶导数
=-1/4(sin(6X+n(π/2))*6^(n)+1/2(sin(4X+n(π/2))*4^(n)+1/2(sin(2X+n(π/2))*2^(n)