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General definition of a derivative

  1. Jun 20, 2005 #1
    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]?
     
    Last edited by a moderator: Jun 20, 2005
  2. jcsd
  3. Jun 20, 2005 #2

    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.
     
  4. Jun 20, 2005 #3
    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:
     
    Last edited: Jun 20, 2005
  5. Jun 20, 2005 #4

    dextercioby

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

    Daniel.
     
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