mat265_masteryexamreview_2012_1

mat265_masteryexamreview_2012_1 - MAT 265 Review Problems...

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MAT 265 Review Problems for Mastery Exam Find the derivatives dy dx of each of the following functions. 1. y 5 x 2 5 x 3 x 2. y x x 2 2 2 3. y x x 1 4. y cos x 1 sin x 2 5. y (17 x 2 5 x ) 50 6. y e 2 x sin(3 x ) 7. y ln(ln x ) e x 2 8. x y 5 10 9. ) cot( x y 10. y ( x 2 1) arctan x 11. y ln 1 x 1 12. y 2 1 x 2 13. y arcsin( x 2 ) 14. y ln(cos x ) 15. y cos 3 x 16. ) 6 csc( ) 3 ln( x x y 17. y x (ln( x ) x ) 18. y e ln x 2 3 x 7 19. y = mx b ( m and b constant) 20. y tan x x 2 1 21. y [arccos x   ] 3 22. y 2 3 x (3 e ) 23. y arctan( e x ) 24. y e x e x 2 25. x e x y ) sec(
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26. y 2 e x e x 27 y ( ax )tan( bx ) ( a and b constant) 28. y 1 1 e x 29. f ( x ) e x x 30. 2 xy 2 y 2 x 31. y A sin( Bx C ) D ( A , B , C and D constant) 32. x y cot 33. y 6 x 3 2 7 x 1 5 1 34. y 3cos(5 x ) 3sin( x 9 ) 35. y 4 3 3 x 2 x 36. y 5 x 3 x 7 37. y tan(6 x ) 38. ) 5 ( cot 1 x y 39. y x x 2 1 2 40. y 1 2 ln x 2 x 41. y 1 2 cos x 1 3 sin x 42. y 2 x 3 ln x 43. y tan(3) e x 44. y sin 2 x cos 2 x x 45. y sin(2 x ) cos(2 x ) 46. y sin x x 2 47. y x tan(sin ) 1 48. 2 y x 2 sin y 49. y sin 3 (3 x 2 2 x 1) 50. y x 2 tan 1 x 51. y 4 x 3 2 x 4 x
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52. y x 3 3 x e 2 53. y 2 x 2 x 5 54. y 1 cos x sin x 2 55. y (3 x 2 x ) 10 56. y e 3 x cos(2 x ) 57. y ln(ln x ) e sin x 58. y 1 3 x 59. y cos x 60.   x x y 1 cos ) 1 ( 2 61. y ln 2 x 2 3 62. y 7 1 x 3 63. y arccos( x 3 ) 64. ) sec( ln x y 65. y sin 2 x 66.   x e y x ln sec 67. y x 2 ( x ln x ) 68. y ln e x 2 4 x 6 69. y = cx d ( c and d constant) 70. y tan x 4 x 2 71. 4 1 )] ( [sec x y 72. y x 4 3 3 4 73. y arctan(ln x ) 74. y 1 2 e x e x 75. x e x y 3 cot 76. y e e x e x 77. y bx tan( cx )( b and c constant) 78. y 4 3 2 e x
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79. f ( x ) x e x 80. 4 xy 3 y 2 = 2 x 81. y A cos( Bx C ) ( A , B , C and D constant) 82. y cos x 83. y 4 3 x
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