Use the table below to evaluate the derivative with respect to x of g of f of 2 times x at x = 1.

__x | 1 | 2 | 3 | 4

f (x) 6 1 8 2

f' (x) 6 1 8 2

g (x) 1 4 4 3

g' (x) 9 5 5 - 4

(g o f) (2x) = g (f (2x))

take derivitive

use chain rule

remember

derivitive of g (f (x)) = g' (f (x)) f' (x)

so

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

at x=1

f (2x) = f (2) = 1

g' (1) = 1

f' (2x) = f' (2) = 1

we get

(1) (1) (2) = 2

it is 2

I hope yo udidn't copy the wrong value for f (x) or f' (x)