# Thread: Help with d ln(p(r)) / d ln(r) ?

1. ## Help with d ln(p(r)) / d ln(r) ?

Hi all

Maybe I'm just being slow but I can't figure out how to work out this differentiation:

d ln (p(r))
---------
d ln(r)

-where p(r) = A*(1+(r/c)^2)^(-3B/2), and A,B,c are known constants. (p(r) is a model for gas pressure in a big ball of gas, if anyone's wondering).

If it was d ln(p(r)) / dr, it wouldn't be a problem...

but I'm not even quite sure what it means to say "d ln(r)". Have never tried differentiating a function with respect to another function before.

Any help would be much appreciated A link to an explanation of how to do this would be especially nice, couldn't find anything on Google...

-Daniel

2. Originally Posted by unclellama
Hi all

Maybe I'm just being slow but I can't figure out how to work out this differentiation:

d ln (p(r))
---------
d ln(r)

-where p(r) = A*(1+(r/c)^2)^(-3B/2), and A,B,c are known constants. (p(r) is a model for gas pressure in a big ball of gas, if anyone's wondering).

If it was d ln(p(r)) / dr, it wouldn't be a problem...

but I'm not even quite sure what it means to say "d ln(r)". Have never tried differentiating a function with respect to another function before.

Any help would be much appreciated A link to an explanation of how to do this would be especially nice, couldn't find anything on Google...

-Daniel
$\displaystyle \frac{df(x)}{dg(x)}= \left[ 1 \left/ \frac{dg}{dx}\right. \right] ~ \frac{df(x)}{dx}$

RonL

3. Thanks a lot, that's exactly what I needed to know

-Daniel