Re: directional derivative,--

In article <462E0BC2.5080309@xxxxxxxxx>, JEMebius <jemebius@xxxxxxxxx>
wrote:

David C. Ullrich wrote:
On Tue, 24 Apr 2007 01:43:40 +0100, JEMebius <jemebius@xxxxxxxxx>
wrote:

What about the well-known rectangular circular half-cone,
the graph of (x, y) -> z = sqrt(x^2 + y^2)?

That has no directional derivative in _any_ (non-zero) direction
(at the origin, which is presumably the point you're talking about.)

At least not according to what I've always thought was the
standard definition, as at

http://en.wikipedia.org/wiki/Directional_derivative



That is absolutely correct, if it is indeed standard to consider only entire
lines through
the point in question. Is it standard in university and college math
curricula?

I think it is, one reason being you want partial derivatives to be the
same directional derivatives in the directions of the axes.

When defining mathematical concepts I want to stay as closely as possible to
everyday
physical reality. So I identified "direction" with "half-line" rather than
with "line".

I did the same thing.
.