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