


Products and QuotientsThe Quotient RuleLet us first consider the derivative of the following quotient:
Now consider the quotient of the following derivatives:
From the above we can see the following important point:
To find the derivative of a quotient we use the following quotient rule:
In words we say: The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all divided by the denominator squared. Click here to see a proof of the quotient rule. ExampleClick on the question marks to see the following example done stepbystep:
Note that the numerator in the quotient rule looks very similar to the product rule. The only difference is that we subtract f(x)g'(x) from g(x)f'(x) rather than add it. Keeping this in mind, there is a visual method for using the quotient rule that is very similar to that for the product rule and can be used as an alternative to memorizing the formula for the quotient rule.
ExampleFind the derivative of ExerciseTry solving these exercises using the quotient rule. Exercise<< The Product Rule  Differentiation Index  Chain Rule >>
