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Like numerator / denominator, but for differentiation.

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    If it helps, they're generally called "infinitesimals" I don't seem to be able to find specific terms for the numerator and denominator... as it's still a division problem, so I'd argue the terms are still apt.
    – Catija
    Commented May 24, 2015 at 20:33
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    The dependent and independent variables respectively. Technically speaking dy/dx isn't a fraction; it's a limit.
    – A.Ellett
    Commented May 24, 2015 at 20:46
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    I think this is on topic here, but would be likely to get better answers, and to get answers more quickly, on the math Stack Exchange site. I think terminology questions are on topic there as well.
    – herisson
    Commented May 24, 2015 at 20:47
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    Here's a related question (it's half of yours) on Math that includes the suggestion differentiand (a neologism) for "that which is to be differentiated", by analogy with other Latin forms like addend = "that which is to be added" and multiplicand = "that which is to be multiplied". math.stackexchange.com/questions/656466/…
    – herisson
    Commented May 24, 2015 at 20:54
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    I'm voting to close this question as off-topic because it is predicated on the misconception that dy/dx is decomposable. Commented May 24, 2015 at 21:36

1 Answer 1

6

dy/dx is a limit in which y represents the dependent variable and x the independent variable. Since it is a limit, technically it is not a fraction.

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  • Is that really what it is, or just what it is equal to? I am not a mathematician, but if I remember correctly there are multiple ways to define differentiation, and not all of them require the concept of a limit.
    – herisson
    Commented May 24, 2015 at 21:04
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    @sumelic The derivative is defined by a limit. It turns out that the derivative of many algebraically defined functions can easily be found by various algebraic rules. But those rules are not what make derivatives what they are; the limit does.
    – A.Ellett
    Commented May 24, 2015 at 21:08
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    @A. Ellet: I understand that the algebraic formulas for finding the derivative don't constitute a definition. But I thought somebody had also figured out a definition based on infinitesimals rather than limits.
    – herisson
    Commented May 24, 2015 at 21:14
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    @sumelic That is true. But infinitesimals are a peculiar area of mathematics and do not form any part of standard mathematics education: whether in advanced mathematics or not. Philosophically infinitesimals are interesting, but they can be viewed as problematic since they are not constructive. So, yes, if you're interested in non-standard mathematics, it is possible to define derivatives differently. But for practical, every day purposes, it's the limit definition which is actually useful.
    – A.Ellett
    Commented May 24, 2015 at 21:21
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    (correction of a previous comment of mine) The words "independent" and "dependent" variables don't really have anything to do with Leibniz notation or the notion of differentiation. Using them here is sort of analogous to looking at "2/3" and saying that 2 is the even number and 3 is the odd number. (also, such usage of "independent" and "dependent" only applies to a limited perspective on variables)
    – user66219
    Commented May 25, 2015 at 6:12

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