# Differential change of variables

1. Dec 29, 2011

### sjw11

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.

Stuart

2. Dec 29, 2011

### SammyS

Staff Emeritus
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 ?

3. Dec 29, 2011

### sjw11

Sammy,

Apologies I forgot to put that in

ψ=rP

p=P not ρ

cheers

4. Dec 29, 2011

### Joffan

Then P = $\frac{ψ}{r}$

$$\frac{∂P}{∂r} = \frac{∂}{∂r}(ψ\cdot\frac{1}{r}) = \frac{1}{r}\cdot\frac{∂ψ}{∂r} + ψ\cdot\frac{∂}{∂r}(\frac{1}{r})$$

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