Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Product and Quotient Rules for Differentiation.

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Presentation transcript:

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Product and Quotient Rules for Differentiation

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 2 Quick Review Find the limits:

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review - Solutions Slide 3- 3

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 4 What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Second and Higher Order Derivatives … and why These rules help us find derivatives of functions analytically in a more efficient way.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 5 The Constant Multiple Rule The Sum and Difference Rule

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 6 Power Rule Trigonometric Rules

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 7 Examples Find the derivative of the following functions:

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 8 Examples - Solutions Find the derivative of the following functions:

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 9 Example Horizontal Tangents A horizontal tangent is where is the slope of the tangent line is equal to 0,

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 10

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide The Product Rule

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Using the Product Rule

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide The Quotient Rule

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Using the Quotient Rule

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example: Finding the Slope of a Graph 1.Find the slope of the graph at the point 2.Find the slope of the graph at the point

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example: Finding the Equation of a Tangent Line 1.Find the equation of the tangent line to the graph at the point 2.Find the equation of the tangent line to the graph at the point

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Second and Higher Order Derivatives

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Second and Higher Order Derivatives

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 2.1 – 2.3

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 2.1 – 2.3

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 2.1 – 2.3

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 2.1 – 2.3

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 2.1 – 2.3

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 2.1 – 2.3