Quotient Rule (Cambridge (CIE) O Level Additional Maths): Revision Note

Quotient rule

What is the quotient rule?

• The quotient rule is a formula that allows you to differentiate a quotient of two functions

  • i.e. one function divided by another

• If where u and v are functions of x then the quotient rule is:

• In function notation, if then the quotient rule can be written as:

• As with the product rule, ‘dash notation’ may be used to make remembering it easier

• Final answers should match the notation used throughout the question

How do I know when to use the quotient rule?

• The quotient rule is used when trying to differentiate a fraction where both the numerator and denominator are functions of

  • if the numerator is a constant, negative powers can be used

  • if the denominator is a constant, treat it as a factor of the expression\

How do I use the quotient rule?

• Make it clear what and are

  • arranging them in a square can help

    • opposite diagonals match up (like they do for product rule)

 STEP 1

 Identify the two functions, and

 Differentiate both and with respect to to find and

 STEP 2

Obtain  by applying the quotient rule formula Be careful using the formula – because of the minus sign in the numerator, the order of the functions is important Simplify the answer if straightforward or if the question requires a particular form