Differential change of variables

[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.

Thanks in advance for all your help

Stuart

 

[SammyS]

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

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 ?

 

[sjw11]

Sammy,

Apologies I forgot to put that in

ψ=rP

p=P not ρ

cheers

 

[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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