Question

If I am given the relationship between g(x) and f(x), how do I find the relationship between g'(x) and f'(x)?
I am given g(x) = f(3x)
What is the relationship between g'(x) and f'(x)?

Answer 1

well if g(x) = f(x), you agree that g ' (x) = f ' (x) right?

Answer 2

Yes

Answer 3

the only thing that's different is the 'x' in f(x) is 3x

Answer 4

so we use the chain rule

g(x) = f(3x)
g ' (x) = f ' (3x)*d/dx[3x]
g ' (x) = f ' (3x)*3
g ' (x) = 3 * f ' (3x)

Answer 5

the notation d/dx[3x] means "take the derivative of 3x with respect to x"

Answer 6

Oh yea, that make a lot of sense. Thank you.

Answer 7

no problem