Question

Chain rule: if F(x) = f(xf(xf(x))), where f(1) = 2, f(2) = 3, f ' (1) = 4, f ' (2) = 5, and f ' (3) = 6, find F ' (1).

Answer 1

Is this the question$$F(x) = f(f(f(x)))$$

Answer 2

\[F(x) = f(f(f(x)))\]$$
F'(x) = f'(f(f(x)))\cdot f'(f(x)) \cdot f'(x)



$$

Answer 3

the book has the question as stated

Answer 4

but i think yours is the same still

Answer 5

is the answer 120?

Answer 6

The notation matters \[
f(xf(xf(x))) \neq f(f(f(x)))\]

Answer 7

\[F'(1) = f'(f(2)) \times f'(2) \times 4 = 120\]

Answer 8

yes that's correct, but the x's in your question are not superfluous.
I think it's meant to be read differently

Answer 9

Ya this is a huge product rule mess if it's stated correctly :) lol