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?

 

[dextercioby]

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

 

[dextercioby]

Abuse of notation,i don't know how much mathematicians do it,but physicists adore it.

Daniel.