1. Chapter 3: Derivatives Section 3.3: Rules for Differentiation
AP CALCULUS AB
Chapter 3:
Derivatives
Section 3.3:
Rules for Differentiation

2. What you’ll learn about
Positive Integer Powers, Multiples, Sums and Differences
Products and Quotients
Negative Integer Powers of x
Second and Higher Order Derivatives
… and why
These rules help us find derivatives of functions
analytically in a more efficient way.

3. Rule 1 Derivative of a Constant Function

4. Rule 2 Power Rule for Positive Integer Powers of x.

5. Rule 3 The Constant Multiple Rule

6. Rule 4 The Sum and Difference Rule

7. Example Positive Integer Powers, Multiples, Sums, and Differences

8. Example Positive Integer Powers, Multiples, Sums, and Differences

9. Rule 5 The Product Rule (Derivative of the Product =
1st *derivative of the 2nd + 2nd *derivative of the 1st)

10. Example Using the Product Rule

11. Rule 6 The Quotient Rule

12. Section 3.3 – Rules for Differentiation
Derivative of the quotient=
Denominator * Derivative of the
Numerator – Numerator * Derivative
of Denominator, all divided by the
Denominator squared.

13. Example Using the Quotient Rule

14. Rule 7 Power Rule for Negative Integer Powers of x

15. Example Negative Integer Powers of x

16. Second and Higher Order Derivatives

17. Second and Higher Order Derivatives

18. Section 3.3 – Rules for Differentiation
Example:

19. You try: Find

20. You try:
Find the equation of the line tangent to the curve at the given point.

21. You try:
Find the fifth derivative of