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Partial and total differentiation

  1. Apr 5, 2014 #1
    You can give me a good examples where ##\frac{\partial}{\partial x}## is different to ##\frac{d}{dx}## ?
     
    Last edited: Apr 5, 2014
  2. jcsd
  3. Apr 5, 2014 #2

    Mark44

    Staff: Mentor

    Comparing these two operators is like comparing apples and oranges.

    ##\frac{d}{dx}## operates on a function of a single variable; e.g., f(x).
    ##\frac{\partial}{\partial x}## operates on a function of two or more variables; e.g., g(x, y).

    If you are given a function of two or more variables, such as f(x, y), but each variable is a function of one variable alone; i.e., f(x(t), y(t)), then it makes sense to talk about the total derivative df/dt.
     
  4. Apr 8, 2014 #3
    But, I never see a total differential wrt x of a scalar or vector function f(x) be different of the partial differential wrt x of same scalar or vector function f(x).
     
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