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Math Help - Derivatives of Inverse Functions

  1. #1
    Senior Member nycmath's Avatar
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    Derivatives of Inverse Functions

    Find (f^-1)' (a) for each function f and real number a.


    (1) f(x) = sqrt(x-4) when a = 2.


    (2) f(x) = cos(2x), Where 0 is less than or equal to x less than or equal to (pi/2). For question 2, a = 1.


    I would like only the steps for each question. Thank you.
    Last edited by nycmath; October 31st 2013 at 10:20 PM.
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  2. #2
    MHF Contributor
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    Re: Derivatives of Inverse Functions

    What have you learned so far? The easiest way to do this is to find the inverse function and take the derivative.

    y = \sqrt{x-4}\Rightarrow x = y^2+4

    y = \cos (2x) \Rightarrow x = \dfrac{1}{2}\cos^{-1}(y)

    For each, find \dfrac{dx}{dy}.
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