Author 
Topic: Derivative help (Read 7426 times) 

Wardub
Junior Member
Gender:
Posts: 130


Derivative help
« on: Jul 21^{st}, 2010, 10:04am » 
Quote Modify

(A^1)' (x) = 1/(A'(A^1(x)) That should read the derivative of A inverse. I'm trying to follow a proof and can't understand how he got this. It seems like it should involve the chain rule. Can someone help me break it down step by step? Thanks.


IP Logged 



0.999...
Full Member
Gender:
Posts: 156


Re: Derivative help
« Reply #1 on: Jul 21^{st}, 2010, 10:18am » 
Quote Modify

Assuming the existence of an inverse of A, we have the equation, A(A^{1}(x)) = x . Now, we implicitly differentiate w.r.t. x and indeed the chain rule implies that (A^{1})'(x)*A'(A^{1}(x)) = 1 . Hence the result. Visually, since the graph of the inverse function A^{1} is a reflection of the initial function A across y = x, if at (a,b) A has slope dy/dx then at (b,a) A^{1} has slope dx/dy.


IP Logged 



