# General definition of a derivative

#### 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 $\Delta y \rightarrow 0$?

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#### dextercioby

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

Daniel.

#### 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:

#### dextercioby

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

Daniel.

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