Question

F(x)=f(f(x)) and G(x)=(F(x))2 and suppose that

f(5)=11,f(11)=2,f′(11)=6,f′(5)=5. What is G'(5) ?

Answer 1

i got F'(5) to be 30 but i'm not getting the right answer for G'(5)

Answer 2

let me check your first one...
\[F(x)=f(f(x)) \\ F'(x)=f'(x) \cdot f'(f(x)) \\ \text{ now replace } x \text{ with 5} \text{ \to find } F'(5) \\ F'(5)=f'(5) \cdot f'(f(5))=5 \cdot f'(11)=5 \cdot 6=30\]
first one looks incredible

Answer 3

what is G(x)?

Answer 4

\[G(x)=(F(x))^2\]

Answer 5

is that right?

Answer 6

\[G'(x)=2 (F(x))^{2-1} \cdot (F(x))'\]
and you already found F'(x) so replace it down here

Answer 7

okay so i got 2(f(f(5))*30 and then 2f(11) * 30 and then 2* 2* 30 and then 120

Answer 8

\[F(x)=f(f(x)) \\ F(5)=f(f(5))=f(11)=2 \\ \\ G'(5)=2F(5)F'(5)=2(2)(30)\]
had to do myself to make sure
yes that looks good :)

Answer 9

ok thanks