1 / 17

Derivatives of Logarithmic Functions

Derivatives of Logarithmic Functions. Objective: Obtain derivative formulas for logs. Review Laws of Logs. Algebraic Properties of Logarithms Product Property Quotient Property Power Property Change of base. Definitions to Remember. Example 1.

kylee-mccarthy
Download Presentation

Derivatives of Logarithmic 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. Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.

  2. Review Laws of Logs • Algebraic Properties of Logarithms • Product Property • Quotient Property • Power Property • Change of base

  3. Definitions to Remember

  4. Example 1 • Does the graph of y = lnx have any horizontal tangents?

  5. Example 1 • Does the graph of y = lnx have any horizontal tangents? • The answer is no. 1/x will never equal zero, so there are no horizontal tangent lines.

  6. Example 2 • Find

  7. Example 3 • Find

  8. Absolute Value • Lets look at • If x > 0, |x| = x, so we have • If x < 0, |x|= -x, so we have • So we can say that

  9. Example 4 • Find

  10. Example 5 • Find

  11. Example 5 • Find • We will use our rules of logs to make this a much easier problem.

  12. Example 5 • Now, we solve.

  13. Logarithmic Differentiation • This is another method that makes finding the derivative of complicated problems much easier. • Find the derivative of

  14. Logarithmic Differentiation • Find the derivative of • First, take the natural log of both sides and treat it like example 3.

  15. Logarithmic Differentiation • Find the derivative of • First, take the natural log of both sides and treat it like example 3.

  16. Logarithmic Differentiation • Find the derivative of

  17. Homework • Pages 247-248 • 1-33 odd

More Related