1. MAT 1221 Survey of Calculus Section 2.2 Some Rules for Differentiation http://myhome.spu.edu/lauw

2. Expectations Use pencils Use “=“ signs and “lim” notation correctly Do not “cross out” expressions doing cancelations Do not skip steps – points are assigned to all essential steps Need the transitional statement: “The equation of the tangent line at…”

3. Reminder WebAssign Homework Read the next section on the schedule

4. Recall The slope of the tangent line of y=f(x) at any given value of x.) Computation of limits are not efficient. We want to have formulas for the derivatives without compute limits.

5. Preview Familiar with the many common notations for derivatives Familiar with the different basic formulas for differentiation

6. Notations The following are common notations for the derivative y=f(x).

7. Constant Function Rule If, then Why?

8. Constant Function Rule If, then Why? 1. Geometric Reason 2. Limit computation

9. Constant Function Rule x y C x

10. Example 1

11. Power Rule If, then (n can be any real number)

12. Power Rule If, then Why? (Can be proved by computing limits) Evidences?

13. 2.1 Example 2 Find the slope of the tangent line of At x=2

14. Example 2

16. Constant Multiple Rule If, then where is a constant

17. Example 3

18. Sum and Difference Rule If, then

19. Example 4

20. Example 5

21. Expectations Use pencils Use “=“ signs