Question

Use Chain Rule to Solve F(x)=f(f(x) and G(x)=(F(x))^2. You also know that f(3)=8 f(8)=3 f'(8)=11 f'(3)=4. Find F'(3) and G'(3) I have been stuck on this for hours.

Answer 1

differentiate F(x)= f(f(x))

Answer 2

F'(x)= f'(f(x)) f'(x)

Answer 3

now at x=3
F'(3)= f'(f(3)) f'(3)

Answer 4

So would it be 4*3*3?

Answer 5

F'(3)= f'(f(3)) f'(3) = f'(8)4= 11*4=44
do the same for other one

Answer 6

fine?

Answer 7

Still a little lost on the G(x) one

Answer 8

So would it be 2(44)*11?

Answer 9

G(x)=(F(x))^2
G'(x)= 2 F(x)* F'(x)
at x=3
G'(3)= 2 F(3)* F'(3)
u know F'(3) =44 from previous question
so u have to find F(3) only

Answer 10

use this for getting F(3)
F(x)=f(f(x)

Answer 11

does it help u?

Answer 12

So wait is it 44*44?

Answer 13

F(3)=f(f(3)) = f(8) =3
so G'(3)= 2 F(3)* F'(3)= 2 *3*44

Answer 14

I get it now thank you so much!

Answer 15

:)