# How do you use the quotient rule to differentiate x^6/(x-6)?

Apr 14, 2016

$f ' \left(x\right) = \frac{5 {x}^{6} - 36 {x}^{5}}{x - 6} ^ 2$

#### Explanation:

Let $f = {x}^{6} \mathmr{and} g = x - 6$

Then$f ' = 6 {x}^{5} \mathmr{and} g ' = 1$

Quotient Rule:
$f ' \left(x\right) = \frac{g f ' - f g '}{g} ^ 2$

$f ' \left(x\right) = \frac{\left(x - 6\right) \left(6 {x}^{5}\right) - \left({x}^{6}\right)}{x - 6} ^ 2$

$= \frac{6 {x}^{6} - 36 {x}^{5} - {x}^{6}}{x - 6} ^ 2$

$= \frac{5 {x}^{6} - 36 {x}^{5}}{x - 6} ^ 2$