$\displaystyle D_r (\frac{2r+3}{3r-2})$

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- Dec 1st 2006, 09:10 PM^_^Engineer_Adam^_^Derivative help
$\displaystyle D_r (\frac{2r+3}{3r-2})$

- Dec 2nd 2006, 12:18 AMCaptainBlack
You need the quotient rule:

$\displaystyle D_r \frac{f(r)}{g(r)}=\frac{g(r)f'(r)-f'(r)g(r)}{[g(r)]^2}$

here:

$\displaystyle f(r)=2r+3$,

$\displaystyle f'(r)=2$,

$\displaystyle g(r)=3r-2$,

$\displaystyle g'(r)=3$

so:

$\displaystyle D_r \left( \frac{2r+3}{3r-2} \right)=\frac{g(r)f'(r)-f(r)g'(r)}{[g(r)]^2}

=\frac{2(3r-2)-3(2r+3)}{(3r-2)^2}=-\frac{13}{(3r-2)^2}

$

RonL - Dec 2nd 2006, 01:37 PMThePerfectHacker
- Dec 2nd 2006, 01:42 PMCaptainBlack