$y=\cos^6x+2\sin^4x\cos^2x-3\sin^2x\cos^4x+\sin^4x$
$y'=6\cos^5x.(\cos x)'+2[4\sin^3x(\sin x)'\cos^2x+\sin^4x.2\cos x(\cos x)']-3[2\sin x(\sin x)'\cos^4x+\sin^2x.4\cos^3x.(\cos x)']+4\sin^3x(\sin x)'$
$=-6\cos^5x\sin x+2.(4\sin^3x\cos^3x-2\cos x\sin^5x)-3(2\sin x\cos^5x-4\cos^3x.\sin^3x)+4\sin^3x\cos x$
$=-6\cos^5x\sin x+8\sin^3x\cos^3x-4\sin^5x\cos x-6\sin x\cos^5x+12\cos^3x\sin^3x+4\sin^3x\cos x$
$=-18\sin x\cos^5x+20\sin^3x\cos^3x-4\sin^5x\cos x+4\sin^3x\cos x$