1. Calculus BC 2014 Implicit Differentiation

2. Implicit Differentiation Equation for a line: Explicit Form Implicit Form Differentiate the Explicit 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 Chain Rule Pretend y is some function like so becomes (A) (B) (C) Note: Use the Leibniz form. Leads to Parametric and Related Rates. Find the derivative with respect to x

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:

9. Why Implicit? Explicit Form:

10. Ex 2 Graph: Plot the Folium of Descartes on your graphing calculator and determine the portion of the folium generated when (a) t 0 Parametric Form:

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

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

13. Higher Derivatives EX: Find the Third Derivative.

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