$g(1) = 3$, $g'(1) = 2$ and $f'(3) = 4$. What is the derivative of $f(g(x))$ at $x = 1$?

Explanation

1. 01

   By the chain rule, $\frac{d}{dx}f(g(x)) = f'(g(x)) \cdot g'(x)$.

2. 02

   At $x = 1$: $f'(g(1)) \cdot g'(1) = f'(3) \cdot 2 = 4 \times 2 = 8$.