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).

Question

owen3 · Answer

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

owen3 · Answer

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

zenmo · Answer

the book has the question as stated

zenmo · Answer

but i think yours is the same still

zenmo · Answer

is the answer 120?

owen3 · Answer

The notation matters $$ 
 f(xf(xf(x))) \neq f(f(f(x)))$$

zenmo · Answer

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

owen3 · Answer

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

zepdrix · Answer

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