1 / 14

2014 Implicit Differentiation

2014 Implicit Differentiation. Calculus BC. 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 >

heinz
Télécharger la présentation

2014 Implicit Differentiation

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. 2014 Implicit Differentiation Calculus BC

  2. 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.

  3. 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)

  4. 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.

  5. Implicit Differentiation (D) Product Rule  (E) Chain Rule

  6. Implicit Differentiation To find implicitly. EX: Diff Both Sides of equation with respect to x Solve for

  7. 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.

  8. Ex 2: < Folium of Descartes >

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

  10. Ex 2 Graph: < Folium of Descartes > Parametric Form: Plot the Folium of Descartes on your graphing calculator and determine the portion of the folium generated when (a) t < -1 ; (b) -1 < t  0 ; (c) t > 0

  11. 2nd Derivatives EX: Our friendly circle. Find the 2nd Derivative. 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.

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

  13. EX: Find the Third Derivative. Higher Derivatives

  14. Last update • 10/19/10 • p. 162 11 – 29 odd

More Related