1 / 13

Chain Rule

Chain Rule. 3.5. Consider:. These can all be thought of as composite functions F(g(x)). Derivatives of Composite functions are found using the chain rule. The Chain Rule. Consider the composition of two functions f ( x ) and g ( x ) given by

oriole
Download Presentation

Chain Rule

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. Chain Rule 3.5

  2. Consider: These can all be thought of as composite functions F(g(x)) Derivatives of Composite functions are found using the chain rule.

  3. The Chain Rule Consider the composition of two functions f(x) and g(x) given by The formula for the derivative of this composition is known as the chain rule. Derivative of the outside times derivative of the inside Chain Rule If y = g(u) and u = f(x) and both of these functions are differentiable, then the composite function y = g[f(x)] is differentiable and

  4. Example: Find the derivative: This may not always be easy to expand Use the chain Rule! Outer Inner

  5. Find derivative of:

  6. Find:

  7. Find derivative of:

  8. Find Derivative of: Chain Rule allows us to use product rule instead of quotient rule! Times the derivative of the second Times the derivative of the first Plus the second First

  9. More Chain Rule!!!!!! Day 2

  10. Find derivative of: Rewrite Chain Rule Simplify

  11. Find: Chain Rule Rewrite

  12. Find derivative of: Rewrite Chain Rule Chain Rule Double angle Formula Sin2u = 2sinu * cosu

  13. Find the slope of the tangent line of:

More Related