anonymous
  • anonymous
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)?
Calculus1
katieb
  • katieb
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jim_thompson5910
  • jim_thompson5910
well if g(x) = f(x), you agree that g ' (x) = f ' (x) right?
anonymous
  • anonymous
Yes
jim_thompson5910
  • jim_thompson5910
the only thing that's different is the 'x' in f(x) is 3x

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jim_thompson5910
  • jim_thompson5910
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)
jim_thompson5910
  • jim_thompson5910
the notation d/dx[3x] means "take the derivative of 3x with respect to x"
anonymous
  • anonymous
Oh yea, that make a lot of sense. Thank you.
jim_thompson5910
  • jim_thompson5910
no problem

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