## kiszer4148 2 years ago What do I do here? A table of values for f,g,f', and g' is given below. x f(x) g(x) f ' (x) g' (x) 1 1 3 3 1 2 2 3 2 1 3 2 1 2 3 A. If h(x)=f(g(x)), h'(3)= B. If h(x)=g(f(x)), then h'(2)=

1. hartnn

can you differentiate h(x) = f(g(x)) using chain rule ? to find h'(x)

2. hartnn

do u know whats chain rule ?

3. kiszer4148

I know the chain rule but I don't understand how I'm supposed to differentiate with no equation

4. hartnn

what definition of chain rule u have with u ?

5. kiszer4148

Let F be the composition of two differentiable functions f and g; F(x) = f(g(x)). Then F is differentiable and F'(x) = f '(g(x)) g '(x) That is textbook definition that I have on me

6. hartnn

you just differentiated f(g(x)) ! h' (x) = [f(g(x))]' = f '(g(x)) g '(x)

7. hartnn

now to get h'(3), just put x=3 in h'(x) what u get ?

8. kiszer4148

So part a would be 9? since g'(3)=3 and f'(g(3) is 3 right?

9. hartnn

yes, correct :)

10. hartnn

now what about [g(f(x))]' using same chain rule

11. kiszer4148

That answer will be 2 right? Since with the chain rule you will get g'(f(x)) f'(x)

12. hartnn

yes, thats also correct :) good work!

13. kiszer4148

Thank you very much for your help. I have another calc problem left on this assignment. Do you mind helping me with that one also by chance?

14. hartnn

ask the question in new post, if i can i'll help :)

15. kiszer4148

Sounds good