1 / 12

Basic Derivatives

Basic Derivatives. Brought To You By:. Tutorial Services. The Math Center. Definition Of A Derivative. The derivative of a function at a point x=a , can be interpreted in several different ways:. Algebraically, the Geometrically as the slope of the tangent line to the graph of at

jonah
Download Presentation

Basic Derivatives

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. Basic Derivatives Brought To You By: Tutorial Services The Math Center

  2. Definition Of A Derivative The derivative of a function at a point x=a, can be interpreted in several different ways: • Algebraically, the • Geometrically as the slope of the tangent line to the graph of at • Functionally as the instantaneous rate of change of at

  3. Applications of Derivatives • Finding the instantaneous velocity of an object at a precise moment in time • Finding the instantaneous rate of change of a function • Finding the slope of the tangent to the graph of a function * NOTE: the derivative symbol can be written as or or

  4. Basic Derivative Formulas • If , where n is a constant, then • If , where c is a constant, then • If , where c is a constant, then Power Rule Constant Rule Power Rule

  5. More basic derivative formulas Logarithm Rule If , then Exponential Rule If , then

  6. Examples Solution: Following the Power Rule, we can now calculate the derivative. Differentiate:

  7. Examples (cont.) Differentiate: Solution: Following the Constant Rule,we can now calculate the derivative.

  8. Examples (cont.) Differentiate: Solution: Following the Power Rule, we can now calculate the derivative.

  9. Examples (cont.) Differentiate: Solution: Following the Logarithm Rule, we can now calculate the derivative. u = x u’ = 1

  10. Examples (cont.) Differentiate: Solution: Following the Exponential Rule,we can now calculate the derivative.

  11. Questions???

  12. Helpful Links • Derivatives and Integrals Handout • Implicit Differentiation Handout • Derivatives Student Handout • Derivatives Quiz

More Related