f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(3x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1).

x 1 2 3 4 5 6
f(x) 0 3 2 1 2 0
g(x) 1 3 2 6 5 0
f '(x) 3 2 1 4 0 2
g '(x) 1 5 4 3 2 0

Question

f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(3x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1).

x	1	2	3	4	5	6
f(x)	0	3	2	1	2	0
g(x)	1	3	2	6	5	0
f '(x)	3	2	1	4	0	2
g '(x)	1	5	4	3	2	0

jim_thompson5910 · Answer

how far did you get?

anonymous · Answer

well i mean i know what to plug in and stuff just not sure how to find the derivative of h(x)

jim_thompson5910 · Answer

I'm assuming you have learned about the chain rule?

anonymous · Answer

would it be g'[f(3x)](f'(3x)) ?

anonymous · Answer

yes i have just not sure about its specifics , would i have to do a double chain rule here because of the f'(3x)?

jim_thompson5910 · Answer

very close

jim_thompson5910 · Answer

you forgot about the inner most part 3x

you derive that to get 3

jim_thompson5910 · Answer

you should get
h ' (x) = g ' [f(3x)]*f ' (3x)*3

anonymous · Answer

got it! :D thank you very much :D

jim_thompson5910 · Answer

what result did you get?

jim_thompson5910 · Answer

you should get a single numeric answer