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Math Help - Rearanging formula

  1. #1
    Junior Member
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    Rearanging formula

    Can anyone please explain how to get from 1 --> 2


    1. Q + r* dQ/dr + q*r = 0




    2. 1/r * d/dr  * r*Q = -q

    Thanks

    Calypso
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  2. #2
    MHF Contributor
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    Quote Originally Posted by calypso View Post
    Can anyone please explain how to get from 1 --> 2


    1. Q + r* dQ/dr + q*r = 0




    2. 1/r * d/dr  * r*Q = -q

    Thanks

    Calypso
    Q+r\frac{dQ}{dr}+qr=0

    \frac{Q}{r}+\frac{dQ}{dr}=-q

    Now, you can continue, using

    \frac{dQ}{dr}=\frac{d}{dr}\left(\frac{Qr}{r}\right  ) and use the quotient rule of differentiation,

    \frac{d}{dr}\left(\frac{u}{v}\right)=\frac{v\frac{  du}{dr}-u\frac{dv}{dr}}{v^2}

    u=Qr,\ v=r gives

    \frac{r\frac{d(Qr)}{dr}-Qr(1)}{r^2}=\frac{1}{r}\frac{d(Qr)}{dr}-\frac{Q}{r}

    Hence,

    \frac{Q}{r}+\frac{dQ}{dr}=\frac{1}{r}\frac{d(Qr)}{  dr}
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  3. #3
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    Great thanks very much
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