Question Detail
Question
Let \( f \) and \( g \) be differentiable functions with \( f(1)=4, g(1)=3, f'(3)=-5, f'(1)=-4, g'(1)=-3, g'(3)=2 \). If \( h(x) = f(g(x)) \), then \( h'(1) = \)?
Correct Answer
Option A is the correct answer.
Detailed Explanation
Using the chain rule: ( h'(x) = f'(g(x)) \cdot g'(x) ). Thus ( h'(1) = f'(g(1)) \cdot g'(1) = f'(3) \cdot g'(1) = (-5)(-3) = 15 ).
Hint
Apply the chain rule formula \( (f \circ g)'(x) = f'(g(x))g'(x) \).