求y=sin^nx cos^nx的导数

y=sin^nx cos^nx
y′=nsin^(n-1)xcosxcos^nx+ncos^(n-1)x(-sinx)sin^nx
=nsin^(n-1)xcos^(n-1)x(cos²x-sin²x)
=nsin^(n-1)xcos^(n-1)cos(2x)