Download presentation

Presentation is loading. Please wait.

Published byTimothy Ward Modified over 6 years ago

1
Homework Homework Assignment #18 Read Section 3.10 Page 191, Exercises: 1 – 37 (EOO) Quiz next time Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

2
Example, Page 191 1. Find the inverse g(x) of with domain x ≥ 0 and calculate g′(x) in two ways, using Theorem 1 and by direct calculation. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

3
Example, Page 191 Use Theorem 1 to calculate g′(x) where g(x) is the inverse of f (x). Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

4
Example, Page 191 9. Let g(x) be the inverse of f (x) = x 3 +2x +4. Calculate g(7) and then calculate g′(7). Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

5
Example, Page 191 Calculate g(b) and g′(b) where g is the inverse of f. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

6
Example, Page 191 17. Let f (x) = x n and g(x) = x 1/n. Compute g′(x) using Theorem 1 and check your answer using the Power Rule. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

7
Example, Page 191 Compute the derivative at the point without using a calculator. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

8
Example, Page 191 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

9
Example, Page 191 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

10
Example, Page 191 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

11
Example, Page 191 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

12
Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Chapter 3: Differentiation Section 3.10: Derivatives of General Exponential and Logarithmic Functions Jon Rogawski Calculus, ET First Edition

13
Rogawski Calculus Copyright © 2008 W. H. Freeman and Company In this section, we consider the derivatives of various exponential and logarithmic functions. First, theorem 1 gives the derivative of a base raised to a power that is a function of x.

14
Example, Page 197 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

15
Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Natural logarithms are frequently used in physics and engineering, and their derivative is found using Theorem 2. Remember that we can only find logarithms of positive numbers.

16
Example, Page 197 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

17
Example, Page 197 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

18
Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Two of the most important calculus facts about exponential functions are given in the following box.

19
Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Applying the Chain Rule to the derivative of the natural log, we have the following equality.

20
Example, Page 197 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

21
Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Recall from Math Analysis the change of base formula for logarithms. From the second equation, if b > 0 and b ≠ 1, then the derivative of log b x is given by:

22
Example, Page 197 Compute the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

23
Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Find the derivatives of the functions in Figure 1.

24
Example, Page 197 Compute the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

25
Example, Page 197 Evaluate the derivative using logarithmic differentiation. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

26
Homework Homework Assignment #19 Read Section 3.11 Page 197, Exercises: 1 – 49 (EOO) Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Similar presentations

© 2022 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google