Answer
$$\frac{dy}{dx}=(x^2+x)^4\sin^7x(5(2x+1)\sin x+8(x^2+x)\cos x)$$
Work Step by Step
$$\frac{dy}{dx}=((x^2+x)^5\sin^8x)'=((x^2+x)^5)'\sin^8x+(x^2+x)^5(\sin^8x)'=
5(x^2+x)^4(x^2+x)'\sin^8x+(x^2+x)^5\cdot8\sin^7x(\sin x)'=
5(x^2+x)^4(2x+1)\sin^8x+8(x^2+x)^5\sin^7x\cos x=
(x^2+x)^4\sin^7x(5(2x+1)\sin x+8(x^2+x)\cos x)$$
