Chapter 4 More Derivatives Section 4 3 Derivatives

Chapter 4 More Derivatives Section 4. 3 Derivatives of Inverse Trigonometric Functions Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 2

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 3

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 4

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 5

What you’ll learn about n n Differentiating inverse functions Graphical interpretation of how the derivative of f is related to the derivative of f - 1 Derivatives of the inverse trigonometric functions Identities for graphing arccot, arcsec, and arccsc functions on a graphing calculator … and why The relationship between the graph of a function and its inverse allows us to see the relationship between their derivatives. Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 6

Derivatives of Inverse Functions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 7

Derivative of the Arcsine Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 8

Example Derivative of the Arcsine Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 9

Derivative of the Arctangent Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 10

Derivative of the Arcsecant Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 11

Example Derivative of the Arcsecant Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 12

Inverse Function – Inverse Cofunction Identities Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 13

Calculator Conversion Identities Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 14

Example Derivative of the Arccotangent Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 15