From: horst.kraemer@snafu.de (Horst Kraemer)
Newsgroups: sci.math
Subject: Re: DIFFERENTIABLE BUT NOT C(1
Date: Mon, 16 Nov 1998 20:42:21 GMT

On Mon, 16 Nov 1998 20:45:09 +0100, David Etxeberria Ciaurri
<poter@mx3.redestb.es> wrote:

> well, i'm about getting mad with this quest; i cannot
> find a function differentiable over an open subspace
> but with non-continuous partial derivatives (i.e not C(1 )
> over the same subspace

        f(0) = 0
	f(x) = x^2*sin(1/x)  otherwise

is differentiable in (-a,a) for every positive a but f'(x) is not
continuous at 0 because 

	f'(0) = 0 ( h*sin(1/h)->0 for h->0 )
	f'(x) = 2x*sin(1/x) - cos(1/x) othewise

and f'(x) takes values outside (-1/2,1/2) in every open interval
containing 0.



Regards
Horst