1. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The Chain Rule OBJECTIVES  Find the composition of two functions.  Differentiate using the Extended Power Rule or the Chain Rule. 4.3

2. Slide 1.7- 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4.3 The Chain Rule Suppose that g(x) is a differentiable function of x. Then, for any real number k,

3. Slide 1.7- 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley If y = f(g(x)), then dy = f '(g(x)) ∙ g '(x) dx Alternate Form of Chain Rule

4. Slide 1.7- 4 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 1: Differentiate 4.3 The Chain Rule

5. Slide 1.7- 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 2:

6. Slide 1.7- 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Ex. 2 Answers:

7. Slide 1.7- 7 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 3: Differentiate Combine Product Rule and Extended Power Rule Simplified: 4.3 The Chain Rule

8. Slide 1.7- 8 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 4: Assume that the total revenue (in dollars) from the sale of x televisions is given by Find the marginal revenue when the following number of televisions are sold. a)100 b)200 c)300 d)Find the average revenue from the sale of x televisions. e)Find the marginal average revenue.

9. Slide 1.7- 9 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Answers: a)$148.78 b)$187.29 c)$214.34 d) e)