Question

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

Answer 1

Answer:

Value of (gof)'(2x)  at x=1 is:

18

Step-by-step 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

Answer 2

(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)