Question

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

Answer 1

(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)

Answer 2

Value of (gof)'(2x) at x=1 is:

18

Explanation:

We have to find the value of:

(gof)'(2x) at x=1

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

When x=1

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

=g'(1)×1×2

=9×2

= 18

Hence, value of (gof)'(2x) at x=1 is:

18