let f ang g be the functions in the table...?

Question

x f(x) g(x) f'(x) g'(x)
1 3 2 4 6
2 1 8 5 7
3 7 2 7 9


-If F(x)= f(f(x)), find F'(2)

-If G(x)= g(g(x)), find G'(3)

please explain....

Answer 1

It's the same concept as your last question.
F(x) = f(f(x))
Use the chain rule to find F'(x)
F'(x) = f'(f(x))*f'(x)
F'(2) = f'(f(2))*f'(2)
ou are given that f(2) = 1 and f'(2) = 5
F'(2) = f'(1)*5
You are given that f'(1) = 4
F'(2) = 4*5
F'(2) = 20
Now you try the other one.

Answer 2

f(f(x))`=f`(f(x)*f`(x)
Therefore, f`(f(2)*f(2)=f`(1)*5=4*5=20
Similarly, G`(x)=g`(g(x))*g`(x) and G`(3)=g`(2)*9=7*9=63