Rearanging formula

**calypso** · March 22nd 2010, 02:49 AM

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

**Archie Meade** · March 22nd 2010, 03:27 AM

Originally Posted by calypso

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,

$\frac{Q}{r}+\frac{dQ}{dr}=\frac{1}{r}\frac{d(Qr)}{ dr}$

**calypso** · March 22nd 2010, 03:31 AM

Great thanks very much

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