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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

    Stuart
     
  2. jcsd
  3. Dec 29, 2011 #2

    SammyS

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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
    Sammy,

    Apologies I forgot to put that in

    ψ=rP

    p=P not ρ

    cheers
     
  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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