quotient is the result of dividing two terms or expressions. e.g. Y12_The_Quotient_Rule_01.gif is a quotient.

To differentiate a quotient the best way is often to use the Quotient Rule.

The Quotient Rule Formula

This states:

Y12_The_Quotient_Rule_02.gif
 

 

The Quotient Rule looks complex, but with practice, which is essential, it should become more straightforward.

Example

Y12_The_Quotient_Rule_03.gif

Alternative Quotient Rule Formula

The Quotient Rule can also be written in Y12_The_Quotient_Rule_04.gif notation:

 

Y12_The_Quotient_Rule_05.gif

Example

Y12_The_Quotient_Rule_06.gif

Note: The derivative of the quotient is undefined for values of x that make v zero.