Answer
$$\frac{dy}{dx}=24x^2(2x^3+5)^3$$
Work Step by Step
$$y=(2x^3+5)^4$$ $$\frac{dy}{dx}=\frac{d(2x^3+5)^4}{dx}$$
Let $u=2x^3+5$ and $y=u^4$. Then, according to Chain Rule, $$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}$$ $$\frac{dy}{dx}=\frac{d(u^4)}{du}\frac{d(2x^3+5)}{dx}$$ $$\frac{dy}{dx}=4u^3\times(6x^2+0)$$ $$\frac{dy}{dx}=4(2x^3+5)^3\times6x^2$$ $$\frac{dy}{dx}=24x^2(2x^3+5)^3$$
