分类：教育/科学
问题：求导数习题y=(sin(x)^n)*cos(nx) 
y=(sin(x)^n)*c(nx)
回答：sin^n(x)]'=nsin^(n-1)(x)cosx
[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 
cos(a+b)=cosacosb-sinasinb