y=sin^n(x)cos nx的导数

题目

y=sin^n(x)cos nx的导数
[sin^n(x)]'=nsin^(n-1)(x)cosx 为什么等号左边变成了等号右边,有公式吗?
[cosnx]'=-nsinnx
y'=[sin^n(x)]'cos nx +[cosnx]'sin^n(x)
=nsin^(n-1)(x)cosxcos nx-nsinnxsin^n(x)
=nsin^(n-1)(x)(coscosnx-sinnxsinx)
=nsin^(n-1)(x)cos(n+1)x

答案