Use the table below to evaluate d/dx [g[f(2x)]] at x= 1

Question

Use the table below to evaluate  d/dx [g[f(2x)]] at x= 1

x | 1 | 2 | 3 | 4

f(x)| 6 | 1 | 8 | 2

f'(x)|1 | 3 | 5 | 7

g(x)|1 | 4 | 4 |3

g'(x)| 4 | 5 | 5 |-4

Answer 1

First, take the derivative using the chain rule twice g’(f(2x))•f’(2x)•2

then plug in x = 1

g’(f(2))•f’(2)•2

use the table to plug in the appropriate values

f(2) = 1

g’(1)•f’(2)•2 Then plug in g’(1) = 4 and f’(2) = 3

4•3•2 = 24