1. MAT 1234 Calculus I Section 2.6 Implicit Differentiation http://myhome.spu.edu/lauw

2. Next… WebAssign 2.6 Quiz on 2.5, 2.6

3. WebAssign Reminder Be sure to simplify your answer. WebAssign accepts unsimplified answers.

4. Preview Introduce a new form of extended power rule (notations changes) Introduce Implicit Differentiation

5. Recall (Extended Power Rule)

9. If y is a function in x, then

10. Recall (Extended Power Rule) Wai, do what you need to do.

11. Example 0

12. The Needs for Implicit Differentiation…

13. Example 1 Find the slopes of the tangent line on the graph i.e. find x y

14. Example 1: Method I Make y as the subject of the equation: x y

15. Example 1: Method I Make y as the subject of the equation: x y

16. Example 1: Method I Make y as the subject of the equation: x y

17. Example 1: Method I Suppose the point is on the upper half circle x y

18. Example 1: Method I Suppose the point is on the lower half circle x y

19. Example 1: Method I Two disadvantages of Method I: 1. ??? 2. ???

20. Example 1: Method II Implicit Differentiation: Differentiate both sides of the equation.

21. Expectation You are required to show the implicit differentiation step

22. Notations

23. Example 2

24. Example 3 Find the slope of the tangent line at.

25. Notations Correct or Incorrect because

26. Example 4