If $h(x) = x^3 \sin(x)$, what is the value of $h'(\pi)$?

Core Concept

Using the product rule, $h'(x) = 3x^2\sin(x) + x^3\cos(x)$. Evaluating at $x=\pi$ gives $3\pi^2(0) + \pi^3(-1) = -\pi^3$.