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

If H(x) = g(f(x)), find H'(1)

I know I have to use chain rule but I am confused by the steps I think I am setting it up wrong.

Answer 1

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

If H(x) = g(f(x)), find H'(1)

Per the Chain Rule: The derivative of a composite function g(f(x)) = g'(f(x)) * f'(x)

Because H(x) = g(f(x)) --> H'(x) = g'(f(x))*f'(x)

Therefore, H'(1) = g'(f(1))*f'(1)

Per the values given: f(1) = 3 and f'(1) = 4

Substitution of the values --> H'(1) = g'(f(1))*f'(1) = g'(3)*(4)

Per the values given: g'(3) = 9

Substitution --> H'(1) = g'(f(1))*f'(1) = g'(3)*(4) = (9)*(4) = 36

Final Answer: H'(1) = 36