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Homework Help: Differentiable functions

  1. Nov 29, 2007 #1
    1. The problem statement, all variables and given/known data
    If f is differentiable at x=0 and g(x) = [f(x)]^2, f(0) = f'(0) = -1, then g'(0) =


    2. Relevant equations
    MC Answers:
    (A) -2 (B) -1 (C) 1 (D) 4 (E) 2


    3. The attempt at a solution

    The only thing I could think of was that if g(x) = (f(x))^2 then g'(0) = (f'(0))^2 and then g'(0) = 1. Does this make sense? I kind of feel like my logic is pseudo math and is giving me an incorrect answer.
     
  2. jcsd
  3. Nov 29, 2007 #2

    rock.freak667

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    Homework Helper

    I would say C) but I can't say if my thinking is correct...it amounts to the same as yours...except for one part
     
  4. Nov 29, 2007 #3

    Avodyne

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    By the chain rule, g'(x) = 2f(x)f'(x).
     
  5. Nov 30, 2007 #4

    HallsofIvy

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    You are right- your logic is pseudo math! :smile:The difficulty is that g'(x) is NOT (f'(x))2. As Avodyne said, you need to use the chain rule: g(x)= u2 and u= f(x). dg/dx= (dg/du)(du/dx).
     
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