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Homework Help: How do I find the solution to this derivative problem?

  1. Feb 22, 2010 #1
    1. The problem statement, all variables and given/known data
    Two functions f and g are such that f(4)=3, f prime (4)= -2, g(4)=7, and g prime (4)=5. Determine (1/g^2) prime(4). By "prime" I mean when there is something that looks like a little "1" exponent on the letter.

    Please help and give clear step by step explanations. Thanks.


    2. Relevant equations
    N/A


    3. The attempt at a solution
    I know what is the quotient and product rules are, but I have no idea how to approach this question.
     
  2. jcsd
  3. Feb 22, 2010 #2
    Have you learned the chain rule yet?

    My hint is: what is the derivative of
    [tex]\frac{1}{[g(x)]^2}?[/tex]
     
  4. Feb 22, 2010 #3
    Is it -2g(x)^-3 x g(x)?
     
  5. Feb 22, 2010 #4
    Hint #2:
    Chain rule: f(g(x)) = f'(g(x))g'(x)

    In this case...
    f(g(x)) = g(x)^-2

    Soooo....
     
  6. Feb 22, 2010 #5
    Exactly. Now evaluate your expression at x=4.

    Also, don't use x for multiplication. * would work better. :)
     
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