Question

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)=

Answer 1

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

Answer 2

do u know whats chain rule ?

Answer 3

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

Answer 4

what definition of chain rule u have with u ?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

yes, correct :)

Answer 10

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

Answer 11

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

Answer 12

yes, thats also correct :) good work!

Answer 13

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?

Answer 14

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

Answer 15

Sounds good