# Math Help - Derivatives of Inverse Functions

1. ## 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.

2. ## 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 $\dfrac{dx}{dy}$.