Answer
$$y'=-12\cos^3(\sin^3x)\sin(\sin^3x)\sin^2x\cos x$$
Work Step by Step
$$y'=(\cos^4(\sin^3x))'=4\cos^3(\sin^3x)\cdot(\cos(\sin^3x))'=
4\cos^3(\sin^3x)\cdot(-\sin(\sin^3x))\cdot(\sin^3x)'=
-4\cos^3(\sin^3x)\cdot\sin(\sin^3x)\cdot3\sin^2x\cdot(\sin x)'=
-12\cos^3(\sin^3x)\sin(\sin^3x)\sin^2x\cos x$$
