The quotient rule says the derivative of the quotient of two functions is "the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the denominator squared." Let's use $N$ and $D$ to denote the functions to help us remember.
$\frac{N}{D}' = \frac{DN' - ND'}{D^2}$
These can be involved algebraically, and typically you will attempt to factor the numerator once you have simplified the terms as much as possible.