Find F'(4) and G'(4)?

Question

Let F(x)= f(f(x))
G(x)= F(x)^2
You also know that
f(4)=7
f(7)=2
f '(7)= 8
f '(4)=7

Answer 1

F'(x)=f'(f(x))f'(x)
F'(4)=f'(f(4))f'(4)
= f'(7)f'(4)
= 8*7 = 56

G'(x)=2F(x)F'(x)
G'(4) = 2F(4) F'(4)
= 2 f(f(4)) F'(4)
= 2 f(7) F'(4)
= 2(2)(56)
= 224

Answer 2

Since F(x) = f(f(x)), then F'(x) = f'(f(x)) * f'(x).
F'(4) = f'(f(4)) * f'(4)...just plug in the numbers and you will have the solution rather quickly.

G(x) = F(x)^2, so G'(x) = 2 * F(x) * F'(x).
To find G'(4), just plug in the numbers again: 2 * F(4) * F'(4).

Given those equations and the known values you listed, you may readily find the answers for which you seek.