FAN and MEDAL!
If h(x) = f[f(x)] use the table of values for f and f ′ to find the value of h ′(1).
Here is the chart given

x f(x) f ′(x)
1 3 2
2 1 5
3 6 7

Question

FAN and MEDAL!
If h(x) = f[f(x)] use the table of values for f and f ′ to find the value of h ′(1).
Here is the chart given

x	f(x)	f ′(x)
1	3	2
2	1	5
3	6	7

anonymous · Answer

$$\left(f(f)\right)'=f'(f)\times f'$$ by the chain rule
you have all the numbers you need to find $$f'(f(1))\times f'(1)$$

trisarahtops · Answer

2(3)*2?

trisarahtops · Answer

@satellite73

anonymous · Answer

let me check

anonymous · Answer

ok actually i do not have to check to know it is wrong

anonymous · Answer

the first part is a composition of functions $$f'(f(1))$$

anonymous · Answer

what is $f(1)$?

trisarahtops · Answer

3

anonymous · Answer

ok so $$f'(f(1))=f'(3)=?$$

trisarahtops · Answer

so you saying it's not like f'(1)* f(1)

anonymous · Answer

no 
there is a product there, but also a composition of functions

anonymous · Answer

$$f'(f(1))\times f'(1)$$

anonymous · Answer

the $\times $ is a multiplication but $$f'(f(1))$$ is a composition of functions 

"f prime of f of 1"

trisarahtops · Answer

sorry I took so long I left my computer for a bit. 
f'(f1) = f'(3)= 7?
@satellite73

trisarahtops · Answer

sorry I meant f'(f(1))= f'(3)= 7

trisarahtops · Answer

@satellite73  ?

anonymous · Answer

yes

anonymous · Answer

then multiply by $f'(1)$ to finish

trisarahtops · Answer

7*2 = 14

trisarahtops · Answer

so 14 is the final anwser correct? @satellite73