1 / 7

Differentiating “Combined” Functions

Differentiating “Combined” Functions. Deriving the Sum and Product Rules for Differentiation. Algebraic Combinations. We have seen that it is fairly easy to compute the derivative of a “simple” function using the definition of the derivative.

sofia
Download Presentation

Differentiating “Combined” 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. Differentiating “Combined” Functions Deriving the Sum and Product Rules for Differentiation.

  2. Algebraic Combinations • We have seen that it is fairly easy to compute the derivative of a “simple” function using the definition of the derivative. • More complicated functions can be difficult or impossible to differentiate using this method. • So we ask . . . If we know the derivatives of two fairly simple functions, can we deduce the derivative of some algebraic combination (e.g. the sum or product) of these functions without going back to the difference quotient? Yes!

  3. The Limit of the Sum of Two Functions

  4. The Limit of the Product of Two Functions

  5. Continuity Required! In the course of the calculation above, we said that Is this actually true? Is it ALWAYS true? x x+h

  6. The Limit of the Product of Two Functions Would be zero if g were continuous at x=a. Is it?

  7. The Limit of the Product of Two Functions g is continuous at x=a because g is differentiable at x=a.

More Related