1 / 9

Derivatives of Log Functions

Derivatives of Log Functions. Lesson 4.5. Problem. Consider f(x) = log a x What if we try to use the definition for derivative using the limit No way to break up this portion of the expression to let h → 0. Possible Solution. We know that the derivative is the "slope function"

elvis-yates
Download Presentation

Derivatives of Log 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 Log Functions Lesson 4.5

  2. Problem • Consider f(x) = logax • What if we try to use the definition for derivative using the limit • No way to break up this portion of the expression to let h → 0

  3. Possible Solution • We know that the derivative is the "slope function" • What if we graph y=ln(x) and check the slopes … plotting them

  4. Slope Results • The table at the right shows the values of theslopes at various x values • What function might this be? • Appears to be

  5. Derivative of the Log Function • For the natural logarithm ln(x) • For the log of a different base loga(x)

  6. Examples • Try these sample problems … find the derivative • Don't forget to use the chain rule where applicable

  7. What About ln(-x)? • Consider it a compound function • Apply the chain rule • Thus we see

  8. Conclusion • We now can say • Apply to finding these derivatives

  9. Assignment • Lesson 4.5 • Page 289 • Exercises 1 – 65 EOO

More Related