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Differentiation, Second Derivative, of Functions Problem

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose f(3)=2 , f'(3)=5 , and f''(3)= -2 . Then d²/dx² (f²(x)) at x=3 is equal to ____?

    A. -20
    B. 20
    C. 38
    D. 42
    E. 10


    3. The attempt at a solution

    I am confused about how to find the function to get the derivative from that function. Any Ideas? Thanks.
     
  2. jcsd
  3. Oct 21, 2009 #2
    You have two choices here: the chain rule and product rule.
     
  4. Oct 21, 2009 #3
    So would the derive of f²(x)= 2f'(x) *1?
     
  5. Oct 21, 2009 #4
    would that be the correct derivative?
     
  6. Oct 21, 2009 #5
    Nope. Remember that the chain rule gives that [f(g(x))]' = f'(g(x)) g'(x).
     
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