## Calculus (3rd Edition)

$-3x^{2}\sin(x^{3})$
Let $g(x)=u= x^{3}$ and $f(u)=y=\cos u$ Then, $y=f(g(x))=\cos(x^{3})$ Using the chain rule, we have $\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}=-\sin (u)\times3x^{2}=-3x^{2}\sin(x^{3})$