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Homework Help: Differential change of variables

  1. Dec 29, 2011 #1
    I am working on an exam question, I have the solution but i can't figure out a step in between,

    I need to show that ∂P/∂r = (1/r)∂ψ/∂r - ψ/r^2

    I am wondering where the - ψ/r^2 comes from. I.e. which rule is this, and sencondly how does this apply to higher order differentials.

    Thanks in advance for all your help

  2. jcsd
  3. Dec 29, 2011 #2


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    Hello Stuart. Welcome to PF !

    Without knowing how P, ψ, and r are related, it will be hard to answer your question.

    Is that P supposed to be ρ ?
  4. Dec 29, 2011 #3

    Apologies I forgot to put that in


    p=P not ρ

  5. Dec 29, 2011 #4
    Then P = [itex]\frac{ψ}{r}[/itex]

    [tex]\frac{∂P}{∂r} = \frac{∂}{∂r}(ψ\cdot\frac{1}{r}) = \frac{1}{r}\cdot\frac{∂ψ}{∂r} + ψ\cdot\frac{∂}{∂r}(\frac{1}{r})[/tex]

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