1. 5 Copyright © Cengage Learning. All rights reserved. Logarithmic, Exponential, and Other Transcendental Functions

2. Exponential Functions: Differentiation and Integration Copyright © Cengage Learning. All rights reserved. 5.4

3. 3 Develop properties of the natural exponential function. Differentiate natural exponential functions. Integrate natural exponential functions. Objectives

4. 4 One of the most intriguing (and useful) characteristics of the natural exponential function is that it is its own derivative. In other words, it is a solution to the differential equation y' = y. This result is stated in the next theorem. Derivatives of Exponential Functions

5. 5 Example 3 – Differentiating Exponential Functions

6. 6 Integrals of Exponential Functions

7. 7

8. 8 Find Solution: If you let u = 3x + 1, then du = 3dx Example 7 – Integrating Exponential Functions