``` wu :: forums (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi) riddles >> putnam exam (pure math) >> Derivative help (Message started by: Wardub on Jul 21st, 2010, 10:04am) ``` Title: Derivative help Post by Wardub on Jul 21st, 2010, 10:04am (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. Title: Re: Derivative help Post by 0.999... on Jul 21st, 2010, 10:18am 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. Powered by YaBB 1 Gold - SP 1.4! Forum software copyright © 2000-2004 Yet another Bulletin Board