MAT 265 - Arizona State University



MAT 265

MASTERY TEST REVIEW

Find the derivative [pic] of each of the following functions.

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. [pic]

11. [pic]

12. [pic]

13. [pic]

14. [pic]

15. [pic]

16. [pic]

17. [pic]

18. [pic]

19. [pic] (a and b constant)

20. [pic]

21. [pic]

22. [pic]

23. [pic]

24. [pic]

25. [pic]

26. [pic]

27. [pic]

28. [pic]

29. [pic]

30. [pic]

31. [pic]

32. [pic]

33. [pic]

34. [pic]

35. [pic]

36. [pic]

37. [pic]

38. [pic]

39. [pic]

40. [pic]

41. [pic]

42. [pic]

43. [pic]

44. [pic]

45. [pic]

46. [pic]

47. [pic]

48. [pic]

49. [pic]

50. [pic]

51. y = arccot(x2)

52. y = arcsec(3x + 2)

53. y = arccsc(ex)

54. y = log(3x - 4)

55. y = log3(x2 + 4x)

56. y = ln(eπ + cos(24))

Answers to problems

Note: There is a reasonable assumption that most of these answers are not incorrect.

1. y' = 10x - 5(1/2)x -1/2 + [pic]

2. y' = 50(17x2 - 5x)49(34x - 5)

3. y' = 2x·2x + x2·2x·ln(2)

4. [pic]

5. y' = [pic]

6. y' = (cos x)([pic]) + (sin x)([pic]2x)

7. y' = (12/5)(3x + 2)-1/5

8. y' = (4/3)[pic]ln(3)[pic]2x - 1)

9. y' = (1/2)[pic]x-1)

10. y' = sec2(2x)[pic]2

11. y' = 2x[pic]tan [pic] + x2[pic]sec2 [pic] [pic] [pic]

12. [pic]

13. y' = [pic]

14. y' = 3[pic]

15. y' = 3sin2(3x2 - 2x + 1)[pic]·(6x - 2)

16. y' = (2x) ·tan-1x + (1 + x2) ·[pic]

17. y' = cos[pic]·(1/2)[pic]

18. y' = (1/2)[pic]·(cos x)

19. y' = a·tan(bx) +(ax)sec2(bx) ·b

20. [pic][pic]

21. y' = [pic] · (6x)

22. y' = -tan x

23. y' = [pic]

24. y'=1· (ln(x) - x) + x · ([pic] - 1)

25. y' = 3·2x+1 · ln(2)

26. y' = m

27. y' = 3(cos-1(x))2[pic]

28. y' = [pic]· ex

29. y' = [pic]+[pic]

30. y' = [pic] - [pic]

31. y' = e3x· 3· (cos([pic]) + e3x· (-sin([pic]))[pic]

32. y' = [pic] ·[pic]

33. [pic]

34. y' = [pic]

35. y' = (ln(x) + 1)·[pic]

36. y' = (-sin x ln(sin x) + [pic])[pic]

37. y' = 6(-3/2)x -5/2 + (7/5)x -4/5

38. y' = -15 sin(5x) + 27 x8 cos(x9)

39. y' = [pic]ln(5)·[pic] + (3/7)x6

40. y' = sec2(6x)·6

41. y' = [pic]·6

42. [pic]

43. y' = [pic] - [pic]

44. y' = 2x·ln(2) + [pic]

45. y' = tan(3) ·ex

46. y' = [pic]

47. y' = [pic]

48. y' = (sec2(sin x)) ·(cos x)

49. y' = [pic]

50. y' = e2x·2·sin(3x) + e2x·3·cos(3x)

51. y' = [pic] ·2x

52. y' = [pic] ·3

53. y' = [pic] ·[pic]

54. [pic]

55. [pic]

56. y' = 0

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