anonymous
  • anonymous
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)=
Mathematics
jamiebookeater
  • jamiebookeater
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hartnn
  • hartnn
can you differentiate h(x) = f(g(x)) using chain rule ? to find h'(x)
hartnn
  • hartnn
do u know whats chain rule ?
anonymous
  • anonymous
I know the chain rule but I don't understand how I'm supposed to differentiate with no equation

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hartnn
  • hartnn
what definition of chain rule u have with u ?
anonymous
  • anonymous
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
hartnn
  • hartnn
you just differentiated f(g(x)) ! h' (x) = [f(g(x))]' = f '(g(x)) g '(x)
hartnn
  • hartnn
now to get h'(3), just put x=3 in h'(x) what u get ?
anonymous
  • anonymous
So part a would be 9? since g'(3)=3 and f'(g(3) is 3 right?
hartnn
  • hartnn
yes, correct :)
hartnn
  • hartnn
now what about [g(f(x))]' using same chain rule
anonymous
  • anonymous
That answer will be 2 right? Since with the chain rule you will get g'(f(x)) f'(x)
hartnn
  • hartnn
yes, thats also correct :) good work!
anonymous
  • anonymous
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?
hartnn
  • hartnn
ask the question in new post, if i can i'll help :)
anonymous
  • anonymous
Sounds good

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