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

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.

Rule 1 Derivative of a Constant Function

Rule 2 Power Rule for Positive Integer Powers of x.

Rule 3 The Constant Multiple Rule

Rule 4 The Sum and Difference Rule

Example Positive Integer Powers, Multiples, Sums, and Differences

Example Positive Integer Powers, Multiples, Sums, and Differences

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

Example Using the Product Rule

Rule 6 The Quotient Rule

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.

Example Using the Quotient Rule

Rule 7 Power Rule for Negative Integer Powers of x

Example Negative Integer Powers of x

Second and Higher Order Derivatives

Second and Higher Order Derivatives

Section 3.3 – Rules for Differentiation Example:

You try: Find

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

You try: Find the fifth derivative of