1. Exam2: Differentiation
Exam-2 Problems
Differentiability
Differentiation
Position function
Find limit
Differentiation:
Direct: Find the g’(2)
Indirect: Find the slope of the tangent line, normal line, rate of change, parallel to the line
Find slope in different ways
Find
Find f’(x)
Vertical or horizontal tangent
others

2. Exam2: Differentiation
Derivative Quotient Rule
Derivative of exponential
Derivative Product Rule
DERIVATIVES OF TRIGONOMETRIC FUNCTIONS:
Implicit diff.
Chain Rule:

3. Chapter3: Differentiation
Exam-2 Problems
The slope of the tangent line
The slope of the normal line
The rate of change

4. Chapter3: Differentiation

5. Chapter3: Differentiation

6. Chapter3: Differentiation

7. Chapter3: Differentiation

8. Sec 3.7: Implicit Differentiation

9. Chapter3: Differentiation

10. Sec 3.7: Implicit Differentiation

11. Sec 3.7: Implicit Differentiation

12. Chapter3: Differentiation

13. Chapter3: Differentiation

14. Chapter3: Differentiation

15. Chapter3: Differentiation

16. Chapter3: Differentiation
Exam-2 Problems
Direct: Find the g’(2)
Indirect: Find the slope….
Find slope in different ways
Find
Find: lim
Find f’(x)
others
(Sketch and find the slopes)

17. Sec 3.9: Inverse Trigonometric Functions

18. Sec 3.9: Inverse Trigonometric Functions

19. Chapter3: Differentiation

20. Chapter3: Differentiation

21. Chapter3: Differentiation

22. Exam2: Differentiation
HOW CAN A FUNCTION FAIL TO BE DIFFERENTIABLE?
Definition:
the curve has a vertical tangent line when x = a
1) f is cont at a 2)

23. Chapter3: Differentiation

24. Chapter3: Differentiation
TERM-121 Exam-2

25. Chapter3: Differentiation
TERM-121 Exam-2

26. Chapter3: Differentiation
TERM-121 Exam-2

27. Chapter3: Differentiation

28. Chapter3: Differentiation

29. Chapter3: Differentiation

30. Chapter3: Differentiation
Exam-2 Problems
Direct: Find the g’(2)
Indirect: Find the slope….
Find slope in different ways
Find
Find: lim
Find f’(x)
others

31. Sec 3.5: Derivatives Of Trigonometric Functions

32. Chapter3: Differentiation

33. Chapter3: Differentiation

34. Chapter3: Differentiation

35. Chapter3: Differentiation
Exam-2 Problems
Direct: Find the g’(2)
Indirect: Find the slope….
Find slope in different ways
Find
Find: lim
Find f’(x)
others

36. Chapter3: Differentiation

37. Chapter3: Differentiation

38. Sec 3.5: Derivatives Of Trigonometric Functions

39. Sec 3.5: Derivatives Of Trigonometric Functions

40. Sec 3.5: Derivatives Of Trigonometric Functions

41. Chapter3: Differentiation
Exam-2 Problems
Direct: Find the g’(2)
Indirect: Find the slope….
Find slope in different ways
Find
Find: lim
Find f’(x)
others

42. Chapter3: Differentiation

43. Chapter3: Differentiation

44. Chapter3: Differentiation

45. Chapter3: Differentiation
TERM-121 Exam-2

46. Chapter3: Differentiation

47. Chapter3: Differentiation
Exam-2 Problems
Direct: Find the g’(2)
Indirect: Find the slope….
Find slope in different ways
Find
Find: lim
Find f’(x)
Others ,

48. Chapter3: Differentiation

49. Chapter3: Differentiation

50. Sec 3.11: Linearization and Differentials

51. Sec 3.11: Linearization and Differentials

52. Sec 3.11: Linearization and Differentials

53. Sec 3.5: Implicit Differentiation

54. Sec 3.5: Implicit Differentiation

55. Sec 3.5: Implicit Differentiation

56. Sec 3.5: Implicit Differentiation

57. Chapter3: Differentiation

58. Sec 3.7: Implicit Differentiation

59. Chapter3: Differentiation

60. Sec 3.7: Implicit Differentiation