(a) If h(x) = f(g(x)), find h'(1). (b) If H(x) = g(f(x)), find H'(1).

Question

f(x) f(1)=3 f(2)=1 f(3)=7

g(x) g(1)=2 g(2)=8 g(3)=2

f'(x) f'(1)=4 f'(2)=5 f'(3)=7

g'(x) g'(1)=6 g'(2)=7 g'(3)=9

(a) If h(x) = f(g(x)), find h'(1).

(b) If H(x) = g(f(x)), find H'(1).

Answer 1

h(x) = f(g(x))

By the Chain Rule, h'(x) = f'(g(x))g'(x)

So, h'(1) = f'(g(1))g'(1) = f'(2)(6) = (5)(6) = 30

Do part (b) in a similar manner.