2. MAT 125 – Applied Calculus 3.2 – The Product and Quotient Rules

3. Today’s Class  We will be learning the following concepts today:  The Product Rule  The Quotient Rule Dr. Erickson 3.2 – The Product and Quotient Rules 2

4. If f and g are both differentiable, then The Product Rule 3 3.2 – The Product and Quotient Rules Dr. Erickson

5. WARNING!!!  The derivative of the product of two functions is NOT given by the product of the derivatives of the functions. Dr. Erickson 3.2 – The Product and Quotient Rules 4

6. 5 Dr. Erickson

7.  Use product rule to find the derivative 3.2 – The Product and Quotient Rules 6 Example 1 Dr. Erickson

8. If f and g are both differentiable, then The Quotient Rule 7 3.2 – The Product and Quotient Rules Dr. Erickson

9. WARNING!!  The derivative of the quotient of two functions is NOT given by the quotient of the derivatives of the functions. Dr. Erickson 3.2 – The Product and Quotient Rules 8

10. 9 Dr. Erickson

11. Example 2 10 3.2 – The Product and Quotient Rules Dr. Erickson  Use the quotient rule to find the derivative

12.  Find the equations of the tangent line and normal line to the curve at the specified point. 3.2 – The Product and Quotient Rules 11 Example 3 Dr. Erickson

13.  Differentiate 3.2 – The Product and Quotient Rules 12 Example 3 Dr. Erickson

14. Example 4 Dr. Erickson 3.2 – The Product and Quotient Rules 13

15. Example 5 Dr. Erickson 3.2 – The Product and Quotient Rules 14

16. More Practice  Find the derivative of each function. Dr. Erickson 3.2 – The Product and Quotient Rules 15

17. Next Class  We will discuss the following concepts:  The Chain Rule  The Chain Rule for Powers of Functions  Please read through Section 3.3 – The Chain Rule in your text book before next class. Dr. Erickson 3.2 – The Product and Quotient Rules 16