1 / 8

5.4 Exponential Functions: Differentiation and Integration

5.4 Exponential Functions: Differentiation and Integration. The inverse of f(x) = ln x is f -1 = e x. Therefore, ln (e x ) = x and e ln x = x. Solve for x in the following equations. Take the ln of both sides. Operations with Exponential Functions.

kuri
Download Presentation

5.4 Exponential Functions: Differentiation and Integration

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 5.4 Exponential Functions: Differentiation and Integration The inverse of f(x) = ln x is f-1 = ex. Therefore, ln (ex) = x and e ln x = x Solve for x in the following equations. Take the ln of both sides.

  2. Operations with Exponential Functions The Derivative of the Natural Exponential Function Differentiate.

  3. Find the relative extrema of Since ex never = 0, -1 is the only critical number. neg. pos. Therefore, x = -1 is a min. by the first derivative test. -1 dec. inc. Minimum @ ?

  4. Integration Rules for Exponential Functions Ex. Let u = 3x + 1 du = 3 dx

  5. Ex. Let u = -x2 du = -2x dx Ex. Let u = 1/x = x-1

  6. Let u = cos x Ex. du = -sin x dx Let u = -x du = -dx -du = dx Ex.

  7. Ex. Ex. Let u = ex du = ex dx

  8. Don’t Want You to Be Bored… • Pg. 356 1, 3, 9, 11, 35-51 odd, 57, 77, 79, 85-93 odd, 99, 101

More Related