1. Calculus Chapter 5 Day 1 1

2. The Natural Logarithmic Function and Differentiation The Natural Logarithmic Function- The number e- The Derivative of the Natural Logarithmic Function 2

3. The Natural Logarithmic Function 3

4. Definition of the Natural Logarithmic Function 4

5. Properties of the Natural Logarithmic Function 5

6. Logarithmic Properties 6

7. 7

8. 8

9. Derivative of the Natural Logarithmic Function 9

10. 10

11. Derivative Involving Absolute Value 11

12. The Natural Logarithmic Function and Integration Log Rule for Integration- Integrals of Trigonometric Functions 12

13. Log Rule for Integration 13

14. Log Rule for Integration 14

15. Practice ▪ Click Here for Assignment 5-1: Assignment 5-1 15

16. Integrals of Trigonometric Functions 16

17. Integrals of the Six Basic Trigonometric Functions 17

18. Inverse Functions Inverse Functions- Existence of an Inverse Function- Derivative of an Inverse Function 18

19. Inverse Functions 19

20. Definition of an Inverse Function 20

21. Reflective Property of Inverse Functions 21

22. Existence of an Inverse Function 22

23. The Existence of an Inverse Function 23

24. Guidelines for Finding the Inverse of a Function 24

25. Derivative of an Inverse Function 25

26. Continuity and Differentiability of Inverse Functions 26

27. The Derivative of an Inverse Function 27

28. Exponential Functions: Differentiation and Integration The Natural Exponential Function- Derivatives of Exponential Functions- Integrals of Exponential Functions 28

29. The Natural Exponential Function 29

30. Definition of the Natural Exponential Function 30

31. Inverse Relationships 31

32. Operations with Exponential Functions 32

33. Properties of the Natural Exponential Function 33

34. Derivatives of Exponential Functions 34

35. The Derivative of the Natural Exponential Function 35

36. Integrals of Exponential Functions 36

37. Integration Rules for Exponential Functions 37

38. Practice ▪ Click Here for Assignment 5-2 Assignment 5-2 38

39. 39

40. 40

41. 41

42. 42

43. Properties of Inverse Functions 43

44. Differentiation and Integration 44

45. 45

46. Integration 46

47. The Power Rule for Real Exponents 47

48. Applications of Exponential Functions 48

49. 49

50. Summary of Compound Interest Formulas 50

51. Practice ▪ Click Here for Assignment 5-3 Assignment 5-3 51