# How do you find the derivative for f(x) =x^6/(x-6)?

$\frac{d}{\mathrm{dx}} \left({x}^{6} / \left(x - 6\right)\right) = \frac{5 {x}^{6} - 36 {x}^{5}}{x - 6} ^ 2$
Using the quotient rule : $\frac{d}{\mathrm{dx}} \left[f \frac{x}{g} \left(x\right)\right] = \frac{g \left(x\right) \cdot f ' \left(x\right) - f \left(x\right) \cdot g ' \left(x\right)}{g \left(x\right)} ^ 2$, we get:
$\frac{d}{\mathrm{dx}} \left({x}^{6} / \left(x - 6\right)\right) = \frac{6 {x}^{5} \left(x - 6\right) - {x}^{6}}{x - 6} ^ 2$
$= \frac{5 {x}^{6} - 36 {x}^{5}}{x - 6} ^ 2$