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Alternative differentiation notation?

  1. Mar 7, 2015 #1
    To express the derivative of a particular function, I have recently come across a "new" notation. For the function x2-3x for example, can you write the derivative operator like this?

    x2-3x dx . I heard this is called the Euler notation, is it valid?
  2. jcsd
  3. Mar 7, 2015 #2

    Simon Bridge

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    ... where?
    Without the context it is very difficult to advise you.

    To be an operator, it has to have some way to recieve the input function and some way to output one. So no, that is not an operator.

    If we put ## y=x^2-3x##, then ##dy = (2x-3)dx## is just the usual use of Liebnitz notation.

    ... people are free to define whatever notation they want and call it any name they like - so long as they spell that out in some sort of preamble and are consistent within the text.

    However you have not described "Euler Notation" as it is usually defined.
  4. Mar 7, 2015 #3


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    If f(x) = x2 - 3x, then currently acceptable forms of indicating the derivative can be noted as:

    f'(x) = 2x - 3, which is read "f-prime of x equals ..." or (Lagrange)

    df/dx = 2x - 3, which is read "the derivative of f with respect to x equals ..." (Leibniz)

    Over the years, especially in the 17th and 18th centuries, calculus notation was in a state of flux (get it?), with different notation being preferred in England to that preferred on the Continent. Scientists in England preferred the dot notation used by Newton, which is commonly seen today for expressions with derivatives taken w.r.t. time.

    Scientists on the Continent preferred the d-notation developed by Leibniz or the prime notation due to Lagrange.

  5. Mar 7, 2015 #4


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    Don't use that notation for the derivative. Regardless what Euler did, that notation means something else now. @SteamKing's link gives the common notations. It says that 'D'is called the Euler notation for the differentiation operator. It is very commonly used.
  6. Mar 8, 2015 #5


    Staff: Mentor

    No, what you have is the differential of the function. If df/dx = x2 - 3x represents the derivative of f with respect to x, then df = (x2 - 3x)dx represents the differential of f.
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