Help on calculus please!

Question

Use the table below to evaluate  at x = 1.

x 1 2 3 4

f(x) 6 1 2 2

f '(x) 6 1 10 2

g(x) 1 4 4 3

g '(x)4 5 7 -4

Answer 1

Using the Chain Rule, d/dx[g(f(2x))] = g'(f(2x))[f(2x)]' = g'(f(2x))f'(2x)(2x)'

= 2g'(f(2x))f'(2x)

So, when x = 1, we get 2g'(f(2))f'(2) = 2g'(1)(1) = 2(4)(1) = 8