1 / 21

Activity: Teacher-Directed Instruction

Activity: Teacher-Directed Instruction. 2013 Implicit Differentiation. Calculus AB. Objective . C: The swbat differentiate implicitly equations in more than one variable. L: the swbat explain to others how to find derivatives of multiple types of problems verbally and demonstratively.

gili
Download Presentation

Activity: Teacher-Directed Instruction

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. Activity: Teacher-Directed Instruction

  2. 2013 Implicit Differentiation Calculus AB

  3. Objective • C: The swbat differentiate implicitly equations in more than one variable. • L: the swbat explain to others how to find derivatives of multiple types of problems verbally and demonstratively

  4. Implicit Differentiation Equation for a line: Explicit Form <One variable given explicitly in terms of the other> Implicit Form <Function implied by the equation>   Differentiate the Explicit < Explicit: , y is function of x > Differentiation taking place with respect to x. The derivative is explicit also.

  5. Implicit Differentiation Equation of circle: To work explicitly; must work two equations Implicit Differentiation is a Short Cut - A method to handle equations that are not easily written explicitly. ( Usually non-functions) Don’t want to solve for y

  6. Implicit Differentiation Find the derivative with respect to x < Assuming - y is a differentiable function of x > Chain Rule Pretend y is some function like so becomes (A) (B) (C) Note: Use the Leibniz form. Leads to Parametric and Related Rates. = =

  7. Implicit Differentiation Find the derivative with respect to x < Assuming - y is a differentiable function of x >

  8. Implicit Differentiation (D) Product Rule

  9. Implicit Differentiation  (E) Chain Rule Product inside a chain

  10. Implicit Differentiation To find implicitly. EX: Diff Both Sides of equation with respect to x Solve for Need both x and y to find the slope.

  11. EX 1: (a) Find the derivative at the point ( 5, 3 ) , at ( -1,-3 ) (b) Find where the curve has a horizontal tangent.  (c) Find where the curve has vertical tangents.

  12. EX 1: (b) Find where the curve has a horizontal tangent. Horizontal tangent has a 0 slope

  13. EX 1:  (c) Find where the curve has vertical tangents. Vertical tangent has an undefined slope

  14. Ex 2: < Folium of Descartes >

  15. Why Implicit? Explicit Form: < Folium of Descartes >

  16. EX: Our friendly circle. Find the 2nd Derivative. 2nd Derivatives NOTICE:The second derivative is in terms of x , y , AND dy /dx. The final step will be to substitute back the value of dy / dx into the second derivative.

  17. EX: Find the 2nd Derivative. 2nd Derivatives

  18. EX: Find the Third Derivative. Higher Derivatives

  19. Last update • 10/19/10 • p. 162 1 – 29 odd

More Related