# Thread: [SOLVED] Differentiation question

1. ## [SOLVED] Differentiation question

All done

2. Originally Posted by dumdidum

Thanks for your help

...I can tell from the looks of it that it's a fairly simple question, but haven't done high school maths in...well, 5 years

Do I simply plug p=A/r back into dP/dr....it seems a little too simple

This was my try:

ρ = A/r
dρ/dr = –A/r^2

dP/dr = – GMρ / r^2
= – (G x M x –A/r^2) / r^2
= (G x M x A/r^2) / r^2
= GMA

Ps = 0
(Ps – Pc)(rs – rc) = (0 – Pc) / r
= –Pc / r
–Pc / r = GMA
Pc / r = – GMA
Pc = – GMAr
You start with:

$\displaystyle \frac{dP}{dr}=-\frac{GM \rho}{r^2}$

Then as $\displaystyle \rho=\frac{A}{r}$ you have:

$\displaystyle \frac{dP}{dr}=-\frac{GMA}{r^3}$

Now just rework the original argument with the new right hand side.

CB

3. Thanks CB. Guess it really was that simple