Answer
$$\frac{dy}{dx}=90x^4(1+\sin^3(x^5))^{11}\sin(x^5)\sin(2x^5)$$
Work Step by Step
$$\frac{dy}{dx}=((1+\sin^3(x^5))^{12})'=
12(1+\sin^3(x^5))^{11}(1+\sin^3(x^5))'=
12(1+\sin^3(x^5))^{11}(3\sin^2(x^5)\cdot(\sin(x^5))')=
36(1+\sin^3(x^5))^{11}\sin^2(x^5)\cos(x^5)(x^5)'=
180x^4(1+\sin^3(x^5))^{11}\sin^2(x^5)\cos(x^5)=
90x^4(1+\sin^3(x^5))^{11}\sin(x^5)\sin(2x^5)$$