1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Liebniz notation

  1. Sep 8, 2007 #1
    1. The problem statement, all variables and given/known data
    In many physics books I have seen the treatment of dx/dy as a fraction dx over dy. For example, if you have an expression for dx and an expression for dy then you just put dx in the numerator and dy in the denominator to get the derivative. THis is also done in the separation of variables technique.

    I have heard that this is not mathematically sound. Is there a rule for when you can treat Liebniz notation like fractions?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 8, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

  4. Sep 9, 2007 #3


    User Avatar
    Science Advisor

    The "Liebniz form" for a derivative: dy/dx is NOT a fraction but it can always be treated like one. The derivative is a limit of a fraction. To prove that any "fraction property" works for a derivative, go back before the liimit, use the fraction property, then take the limit.

    That's why the notion of "differentials", defining "dy" and "dx", if only symbolically, that Gokul43201 was referring to, is so powerful.
  5. Sep 9, 2007 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Remember, though, that the derivative is NOT in general a fraction; this is highlighted by the behaviour of partial derivatives:

    let F(x,y) be a differentiable function; x=X(y).

    Thereby, we have:

    Here, the relationships between the pseudo-fractions is NOT that which might be "predicted" by common fraction arithmetic.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook