# How do you use the quotient rule to find the derivative of y=(ax+b)/(cx+d) ?

Jul 29, 2014

$y ' = \frac{a d - b c}{c x + d} ^ 2$

Using Quotient Rule,

$y = f \frac{x}{g} \left(x\right)$, then y'=(f'(x)g(x)−f(x)g'(x))/(g(x))^2

$y = \frac{a x + b}{c x + d}$

differentiating both sides with respect to x,

$y ' = \frac{\left(a x + b\right) ' \left(c x + d\right) - \left(a x + b\right) \left(c x + d\right) '}{c x + d} ^ 2$

$y ' = \frac{a \left(c x + d\right) - \left(a x + b\right) c}{c x + d} ^ 2$

$y ' = \frac{a d - b c}{c x + d} ^ 2$