F.4 Maths Differentiation

Question
Given: G(x) = g[f(x)] and f(1) = 2
If f'(x) = 3 at x = 1, and g'(x) = 5 at x = 2,
find G'(x) at x = 1.

Solution

The question means f'(1) = 3, g'(2) = 5 and asks to find G'(1).

G(x) = g[f(x)]

By chain rule, G'(x) = g'[f(x)] * f'(x)

Therefore,

G'(1) = g'[f(1)] * f'(1)
　　= g'[2] * 3
　　= 5 * 3
　　= 15