求y=sin^nx cos^nx的导数nsin^(n-1)x cos^(n+1)x-nsin^(n+1)x cos^(n-1)x

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求y=sin^nx cos^nx的导数
nsin^(n-1)x cos^(n+1)x-nsin^(n+1)x cos^(n-1)x

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)