MAT 125 Applied Calculus

MAT 125 Applied Calculus3.2 The Product and Quotient Rules1Todays ClassWe will be learning the following concepts today:The Product RuleThe Quotient Rule

Dr. Erickson3.2 The Product and Quotient Rules22If f and g are both differentiable, thenThe Product Rule

33.2 The Product and Quotient RulesDr. EricksonWARNING!!!The derivative of the product of two functions is NOT given by the product of the derivatives of the functions.

Dr. Erickson3.2 The Product and Quotient Rules4

3.2 The Product and Quotient Rules5

Dr. Erickson

Use product rule to find the derivative3.2 The Product and Quotient Rules6Example 1

Dr. EricksonIf f and g are both differentiable, thenThe Quotient Rule

73.2 The Product and Quotient RulesDr. EricksonWARNING!!The derivative of the quotient of two functions is NOT given by the quotient of the derivatives of the functions.

Dr. Erickson3.2 The Product and Quotient Rules8

3.2 The Product and Quotient Rules9

Dr. Erickson

Example 2

103.2 The Product and Quotient RulesDr. EricksonUse the quotient rule to find the derivativeFind the equations of the tangent line and normal line to the curve at the specified point.3.2 The Product and Quotient Rules11Example 3

Dr. EricksonDifferentiate3.2 The Product and Quotient Rules12Example 3

Dr. EricksonExample 4Dr. Erickson3.2 The Product and Quotient Rules13

Example 5Dr. Erickson3.2 The Product and Quotient Rules14

More PracticeFind the derivative of each function.Dr. Erickson3.2 The Product and Quotient Rules15

Next ClassWe will discuss the following concepts:The Chain RuleThe Chain Rule for Powers of Functions

Please read through Section 3.3 The Chain Rule in your text book before next class.

Dr. Erickson3.2 The Product and Quotient Rules16Product RuleMatheatre & Know TheatreCalculus: The Musical! 2nd Edition, track 6/15, disc 1/12010Mathematics95034.93eng - Original Melody by: Meredith Wilson. Performed by Sadie Bowman & Marc Gutman.eng - iTunNORM 00000D14 00000CB2 000065F9 00006A85 000058B5 0000FD83 00007C42 00007B37 0000C55E 0000DB69Matheatre & Know TheatreCalculus: The Musical! 2nd Edition, track 7/15, disc 1/12010Mathematics32130.879eng - iTunNORM 00000A69 00000890 00003D85 00003F2F 0000474A 00003F7D 00007B30 00007C6B 0000414E 00003F7Deng - Original Melody by: Friedrich Wilhelm Mller. Performed by: Rosalie Norris, Marc Gutman, Joe McMorrow, Caleb Lanners.