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Math Help - Show how this derivative is computed

  1. #1
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    Show how this derivative is computed

    Good morning all, I hope you can help. I am following a book I bought on Astronomy and have come to a section which is quite maths intensive but seems to jump from one equation to the next, thus I have the start and the answer but would like to know how the part in the middle is worked out. One such problem that is taking up much of my time is what seems to be a simple derivative, but my skills in this are somewhat basic as its been long time since I was last at school. I need to get from

    ω = √(GM/r)

    to

    ∂ω/∂r = (GM)^{1/2}(-(3/2)r^{-5/2})


    Its not really important for following the book but I would very much like to understand how things go from one step to another and not just be given the answer.

    Thanks in advance for any help.

    Rod.
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  2. #2
    A Plied Mathematician
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    Ok. There's really only a couple of steps to doing this. If you understand that the power rule for derivatives works on fractional exponents, you're essentially done.

    \omega=\sqrt{GM}\sqrt{\frac{1}{r^{3}}}=\sqrt{GM}r^  {-3/2}.

    Hence,

    \frac{\partial \omega}{\partial r}=\sqrt{GM}\left(-\frac{3}{2}\right)r^{-5/2}.

    Done.
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  3. #3
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    Good morning Ackbeet and thank you for a very speedy reply, seeing it now like this the penny has finally dropped, thank you again.

    Best Regards

    Rod.
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  4. #4
    A Plied Mathematician
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    You're welcome. Have a good one!
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