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Math Help - Help with d ln(p(r)) / d ln(r) ?

  1. #1
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    Feb 2008
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    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
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  2. #2
    Grand Panjandrum
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    Nov 2005
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    someplace
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    Quote Originally Posted by unclellama View Post
    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
    \frac{df(x)}{dg(x)}= \left[ 1 \left/  \frac{dg}{dx}\right. \right] ~ \frac{df(x)}{dx}

    RonL
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  3. #3
    Newbie
    Joined
    Feb 2008
    Posts
    4

    Thumbs up

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

    -Daniel
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