# How do you differentiate f(x)=(ax+b)/(cx+d)?

$f ' \left(x\right) = \frac{a d - b c}{c x + d} ^ 2$
${\left(\frac{f}{g}\right)}^{'} = \frac{f ' \cdot g - f \cdot g '}{{g}^{2}} , \setminus g \ne 0$
$f \left(x\right) = \frac{a x + b}{c x + d}$
$f ' \left(x\right) = \frac{\left(a x + b\right) ' \left(c x + d\right) - \left(a x + b\right) \left(c x + d\right) '}{c x + d} ^ 2 = \frac{a \left(c x + d\right) - \left(a x + b\right) c}{c x + d} ^ 2 = \frac{a d - b c}{c x + d} ^ 2$