1. 5.4: Exponential Functions: Differentiation and Integration
Mt. Rushmore, South Dakota
5.4: Exponential Functions: Differentiation and Integration
Greg Kelly, Hanford High School, Richland, Washington
Photo by Vickie Kelly, 2007

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

3. The inverse of is

4. Solve

5. Solve

6. Operations with Exponential Functions:

7. 1. The domain of is
2. is continuous, increasing and one-to-one.
3. is concave upward on its entire domain. 4.

8. Find the derivative of

10. is its own derivative!
If we incorporate the chain rule:

11. Find the derivative of
Find the derivative of

12. Find the relative extrema of

13. Normal Probability Density Function:
(Bell-shaped curve)
General Form of Normal Probability Density Function:

14. Integrals of Exponential Functions:

21. Homework 5.4 (page 358) #1 – 5 odd 11 – 15 odd 39 – 61 odd