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Derivative notation

  1. May 6, 2010 #1
    Hi, this may seem like a silly question but here goes :
    Is there any difference between writing [tex]\partial x[/tex] and [tex]d x[/tex] when referring to partial derivatives? I've always used the simple [tex]d x[/tex] for both because I don't like drawing the curvy d. To me, [tex]\partial N / d x[/tex] and [tex]d N / d x[/tex] are the same really.

    However, if in an exam I was asked to state a theorem (say Green's theorem), should I use the partial derivative symbol when writing the equation?
    How about when I actually use the theorem?]
     
  2. jcsd
  3. May 6, 2010 #2

    Mark44

    Staff: Mentor

    They aren't the same, so you shouldn't use the straight derivative when a partial derivative is called for. Also, don't mix the notation. The partial of f with respect to x is written as
    [tex]\frac{\partial f}{\partial x}[/tex]
    not as
    [tex]\frac{\partial f}{dx}[/tex]

    Here f would be a function of two or more variables, such as f(x, y) = 2x + 3y2. Assuming that x and y are independent, it wouldn't make any sense to talk about df/dx.

    For this simple example,
    [tex]\frac{\partial f}{\partial x} = 2[/tex]
    and
    [tex]\frac{\partial f}{\partial y} = 6y[/tex]

    If you don't like this style of notation, there's another that is used, with subscripts. fx represents the partial of f with respect to x. In the example I gave, fx = 2 and fy = 6y.

     
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