Question

Use the following table to find the value of h ′(3) if h(x) = g[f(x)]:

Answer 1

I got this far:
g'(f(3))*f'(3)
g'(4)*f'(7)
(2)*-- and that's where it leaves off because the table has no value for 7.
Does this mean I multiply 2 times 7 even though it's really (2)*f'(7)?

Answer 2

yes.

your first step

g'(f(3))*f'(3)

is correct

since f(3) = 4, g'(f(3)) = g'(4) = 2

and

f'(3) = 7

so

g'(f(3))*f'(3)

becomes

(2)(7)

Answer 3

Thank you! It makes soon much more sense. I think I was overcomplicating things because the g'(f(3)) has more steps than the second part, but I understand it clearly now.