Differentiable functions $f$ and $g$ have $g(1) = 2$, $g'(1) = -4$, $f'(1) = 7$ and $f'(2) = 3$. What is the derivative of $f(g(x))$ at $x = 1$?

Explanation

1. 01

   $\frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x)$.

2. 02

   At 1: $f'(g(1)) \cdot g'(1) = f'(2) \times (-4) = 3 \times (-4) = -12$.