# Rearanging formula

• Mar 22nd 2010, 02:49 AM
calypso
Rearanging formula
Can anyone please explain how to get from 1 --> 2

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

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

Thanks

Calypso
• Mar 22nd 2010, 03:27 AM
Quote:

Originally Posted by calypso
Can anyone please explain how to get from 1 --> 2

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

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

Thanks

Calypso

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

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

Now, you can continue, using

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

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

$\displaystyle u=Qr,\ v=r$ gives

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

Hence,

$\displaystyle \frac{Q}{r}+\frac{dQ}{dr}=\frac{1}{r}\frac{d(Qr)}{ dr}$
• Mar 22nd 2010, 03:31 AM
calypso
Great thanks very much