General definition of a derivative

  • Thread starter cscott
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I was told that the general definition of a derivative is

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

but why can't it work when [itex]\Delta y \rightarrow 0[/itex]?
 
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dextercioby

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


Daniel.
 
783
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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 :frown:
 
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dextercioby

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

Daniel.
 

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