1. The Quotient Rule
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2. The Quotient Rule
The Quotient Rule is used when there are two or more functions being divided.
The derivative of (f(x)/g(x)) is given by the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
The order in which you derive when using the Quotient Rule is very important, you must derive in the exact order the rule says to, otherwise the result will not be right.

3. EXAMPLE 1
Quotient Rule:

4. CONTINUED
Applying the Quotient Rule:
Combine like terms and simplify:

5. EXAMPLE 2
Rewrite:
We know:

6. CONTINUED
Applying the Quotient Rule:
Simplifying:

7. CONTINUED

8. PRACTICE SAMPLE
We know:

9. CONTINUED
Applying the Quotient Rule:
Simplifying:

10. CONTINUED

11. PRACTICE SAMPLE We begin by applying the Product Rule:
From the equation, we can see that there are two functions being multiplied, while two are being divided, so we can use the Product Rule in combination with the Quotient Rule to solve the problem.
We begin by applying the Product Rule:

12. CONTINUED
We now apply the Quotient Rule for
Combined result:

13. CONTINUED
Simplify:

14. CONTINUED

15. QUESTIONS

16. Quotient Rules Links Quotient Rule Workshop Handout
Product and Quotient Rules Handout
Product Rule Workshop