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Inverse Derivative Proof

  1. Feb 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Assume f ^-1 (inverse) has a derivative. Use the chain rule to prove that
    (f^-1)' (f(x)) = 1/f'(x)

    2. Relevant equations

    No real equations other than definition of chain rule.

    3. The attempt at a solution

    I'm not sure how to start other than with the definition of (f^-1) (f(x)) = x
  2. jcsd
  3. Feb 14, 2010 #2
    You have two ways of computing ((f^-1)' (f(x)))'. You could differentiate the composite function using the chain rule, or differentiate x = (f^-1)' (f(x)) directly. How do the answers compare?
  4. Feb 14, 2010 #3
    Thanks for your help, I used the chainrule and figured it out.
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