Question

if g(f(x))=x, g(5)=2 and g'(5)=14, then f'(2) is ?? help, please!

Answer 1

Do you know chain rule

Answer 2

yes, isnt it nu'u^n-1

Answer 3

(g(f(x)))'=g'(f(x))f'(x)

Answer 4

So if we differentiated one side you must do the same to the side

Answer 5

Other side*

Answer 6

What is f(2)?

Answer 7

wait...how would i plug that in? so would it be g(f(x))'=14(x)(2)??

Answer 8

Ok no . Do you know how to find f(2)?

Answer 9

no

Answer 10

So we have g(f(x))=x

Answer 11

Plug in x=2

Answer 12

So we have g(f(2))=2. Assuming g has an inverse we could say f(2)=g^(-1)(2). But we know g(5)=2 so g^(-1)(2)=5. So we have f(2)=5 right?

Answer 13

Now back to the derivative part we had g'(f(x))f'(x)=1

Answer 14

Now plug in 2 for x

Answer 15

So you would have g'(f(2))f'(2)=1

Answer 16

War is f(2) again ?.

Answer 17

What*

Answer 18

We almost there

Answer 19

All we have to do is plug in