wu :: forums
wu :: forums - Derivative help

Welcome, Guest. Please Login or Register.
Nov 26th, 2021, 3:10pm

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   putnam exam (pure math)
(Moderators: william wu, Eigenray, Icarus, Grimbal, SMQ, towr)
   Derivative help
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Derivative help  (Read 7363 times)
Wardub
Junior Member
**





   


Gender: male
Posts: 130
Derivative help  
« on: Jul 21st, 2010, 10:04am »
Quote Quote Modify 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: male
Posts: 156
Re: Derivative help  
« Reply #1 on: Jul 21st, 2010, 10:18am »
Quote Quote Modify 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
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright 2000-2004 Yet another Bulletin Board