2. 2-2: Differentiation Rules Objectives: Learn basic differentiation rules Explore relationship between derivatives and rates of change © 2002 Roy L. Gover (www.mrgover.com)

3. Basic Differentiation Rules 1.Constant Rule The derivative of a constant function is 0. There is no rate of change.

4. Let’s prove it. Duh…

5. Find the following derivatives using the definition

7. Basic Differentiation Rules 2. Power Rule Where a & n are real numbers and n is rational

8. Warm-Up Find the derivative using the definition (sometimes called the limit of the difference quotient) and the power rule. Confirm that you get the same answer.

9. Basic Differentiation Rules 3. Constant Multiple Rule Where c is a constant

10. Basic Differentiation Rules 3. Constant Multiple Rule Note: alternate notation is the same as

11. Basic Differentiation Rules 3. Sum or Difference Rule The derivative of the sum or difference is the sum or difference of the derivatives

12. Basic Differentiation Rules 4. Derivatives of Sine & Cosine

13. Prove it! Now! 4. Derivatives of Sine & Cosine

14. Example Find the derivative, if it exists: We used what rule(s)?

15. Example Find the derivative, if it exists: We used what rule(s)?

16. Example Find the derivative, if it exists: We used what rule(s)?

17. Example Find the derivative, if it exists: We used what rule(s)?

18. Try This Find the derivative: First write as then use the power rule:

19. Try This Find the derivative: First write as_____, then…

20. Try This Find the derivative: First write as_____, then…

21. Example Find the slope of at x = x =2 2 x =-1

22. Review Point-Slope Form:

23. Review Slope-y intercept Form:

24. Example x =2 Find the equation of line tangent to at x =2

25. Try This Find the equation of line tangent to at x =1 x =1

26. Example Find the derivative, if it exists: We used what rule(s)?

27. Try This Find the derivative, if it exists:

28. Example Find the derivative, if it exists:

29. Important Idea The slope of the sin function at a point is the value of the cos function at the point

30. Example If an object is dropped, its height above the ground is given by 1. Find the average velocity between 1 and 3 seconds. 2. Find the instantaneous velocity at 3 seconds.

31. Example If an object is dropped, its height above the ground is given by 1. Find the average velocity between 1 and 3 seconds.

32. Example If an object is dropped, its height above the ground is given by 2. Find the instantaneous velocity at 3 seconds.

33. Lesson Close This lesson demonstrated the use of several differentiation rules. There will be others in future lessons. You must memorize these rules.

34. Assignment 123/1-47 odd & 71