1 / 41

Logarithmic Properties & Derivative of Inverse Functions

Explore logarithmic properties for positive numbers and rational exponents, including ln(e) = 1 and ln(1) = 0. Learn how to find the derivative of an inverse function using implicit differentiation and inverse functions. Understand the relationship between inverse functions and reciprocal slopes in their graphs.

minnie
Download Presentation

Logarithmic Properties & Derivative of Inverse Functions

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. Chapter 5

  2. Logarithmic Properties

  3. If a and b are positive numbers and n is rational, then the following properties are true: 1. ln(e) = 1 2. ln(1) = 0 3. ln(ab) = lna + lnb 4. ln( )= nlna 5. ln( )= lna – lnb

  4. Derivative of an Inverse Function

  5. To find the derivative of an inverse function: • Find inverse: Switch x and y • Find derivative: Use implicit differentiation • Solve for y: Use inverse function • Substitute y into derivative

  6. Graphs of inverse functions have reciprocal slopes

  7. Graphs of inverse functions have reciprocal slopes

More Related