General definition of a derivative

1. Jun 20, 2005

cscott

I was told that the general definition of a derivative is

$$f'(x) = \lim_{\Delta x \rightarrow 0} \frac{\Delta y}{\Delta x}$$
(supposed to be delta y over delta x, but I can't make the latex work )

but why can't it work when $\Delta y \rightarrow 0$?

Last edited by a moderator: Jun 20, 2005
2. Jun 20, 2005

dextercioby

Because the function is $y=y(x)$,so it's natural to consider the limit on the "x" (variable's) axis.

Daniel.

3. Jun 20, 2005

cscott

Oh, alright.

Another thing, what is f(x) = y or y(x) = y in normal notation? I thought f(x) replaced y, but the fuction y = y doesn't make sense, does it? I mixed up

Last edited: Jun 20, 2005
4. Jun 20, 2005

dextercioby

Abuse of notation,i dunno how much mathematicians do it,but physicists adore it.

Daniel.