The quotient rule is used when two functions are divided – they form a quotient of the form

The Quotient Rule:

If a function h consists of two simpler functionsandwiththen

(1)

Proof:

At this point we perform the sort of trick common in maths. We takefrom the first term and add it to the second. We can then factorise and simplify.

andand if we we letthen in the denominator,We then obtain (1).

Example: Differentiate

It is a good habit to get into to write downand then you can just substitute them into the expression for

Example: Differentiate