Question

Suppose that h(x)=(fog)(x)=f(g(x)) and that the following hold:?

f(2) = 8, g(2)=2, f'(2)=1/2, g'(2)= -3, f(3)=3, g(3)=2, f'(3)=2

a) What is the derivative of f(g(x)) at x =2?
b) If the derivative of f(g(x)) equals 3 at x=3, what is g'(3)?

Answer 1

[f(g(x))]' = f'(g(x)) * g'(x)
[f(g(2))]' = f'(g(2)) * g'(2)
= f'(2) * g'(2)
= (1/2) * (-3)
= -3/2

Answer 2

that's a...

Answer 3

The question may be asking if it's f ' (g(x)) though.

Answer 4

If that's the case, f ' (g(2)) = f ' (2) = 1/2

Answer 5

f(g(3))]' = 3 = f'(g(3)) * g'(3)
3 = f'(2) * g'(3)
3 = (1/2) * g'(3)

so g'(3) = 6

Answer 6

Thanks! What rule did you incorporate in there?

Answer 7

just the chain rule and only the chain rule...

Answer 8

Oh, I had used the product rule in mine for some reason. Anyway, thank you so much!

Answer 9

yw....:)