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

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Presentation transcript:

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

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

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

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

5 Dr. Erickson

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

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

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

9 Dr. Erickson

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

 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

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

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

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

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

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