Ejercicios de derivadas

Guia Derivadas Calcule la derivada de las siguientes funciones: 1. y = mx + b 2. s = 2t + t2 3. u = 4v 2 + 2v 3 4. = 2 +1 At + B Ct + D

5. f (t) = 6. y =

x3 + 1 x x 7. f (x) = 2 x +1 8. y= (a 9. y = b )2 x a + bx2 1 x2 (x2 + 1)2 p 7x p + 8 7 x3 3 4 x

10. f (x) =

3x3 11. f (x) = p 5 x2 12. y = ex 3x + 2

13. f (x) = ln(x2 + x) p 14. y = a2 x2 p 2 x p 15. f (x) = 2 x r 1 cx16. y = 1 + cx ! r a + bt 17. s = ln a bt 18. y = 2 ex ex 1 ex + 1

19. f (x) = 20. y =

ln(t2 ) t2 5

21. f (x) = 3x2 + x

1

22. f (x) = (x 2)2 (x + 1) p 4+ x 23. y = 2 x +1 p 24. y= (5 x 3)ex 25. y = 2x(x + 1) x2 2 t 2 t+1
2

26. f (t) = 27. =

1+

28. r(s) = 2s3 + 9s2 + 12s + 1 29. y = (3x2 30. y = 2x (2x p 1)(5x + 2) 5x2 + x3 8)(3x 4) 2x + p 3 x 1 x (x2 + 1)(3x +4)

31. f (x) =

32. g(t) = (t2 + 1)ln(t) 33. y = 3x2 5 x4
5

34. y = x2 e x5 35. f (x) = ex ln(x2 ) 36. g(x) = (x2 + 1)ex r u 1 37. v = u+1 38. xy + x y=3 39. y = ln( x ) 3 40. y = ax2 +bx + c 41. f (x) = 5x 42. f (t) = 2t2 43. f (x) = p x3 + 3x4 3t3 2x 3 t
1 2

3+ 4x a

3x2

44. y = ax2 45. y = x + 46. f (x) =

2 3 + 2 x x x 3 2

2 3x2

47. y =

1 1 + 2 t t p p3 2 48. f (t) = 2 t + 4 2 49. y = x x2 2 x +1 1 x2
2

2

50. f (x) =

51. f (x) = x + ex 52. y =

(2x + 7)(x2 + 3) 3x + 5 p 1 53. f (x) = x3 + p x3 54. y = 55. y = ex 2x + 3 ln x 7 ln xx

56. y =

57. f (x) = (x3 + x)4 58. y = e3x+5 59. f (t) = 60. f (x) = 61. f (x) = 1 (2t + 3)5 ex x2 1 x2

1 62. f (x) = p x p 8 63. y = x x2 64. g(t) = 4t11 65. y = 3 x2 1 x x+1 p 7 2 t+t

66. f (x) =

67. f (x) = x3 ex 68. f (x) = ln(x2 + 1) 69. y = 8 3x x(x 2) 3

70. f (x) = (3x2 2)5 r 1 x 71. f (x) = 1+x 72. f (x) = (1 + x + x2 )3 73. y = 1 x 1 + 2 (x 1)2 + 3 (x 1)374. y = ln(x2 ) 75. f (x) = 76. y = ex x2

2 1 + ex

77. y = 2x2 (x2 + x)2 78. f (x) = (3x2 1)(2x3 + 1) x 4x)(4x3 + 5x2 )

79. y = (2x + 3)(3x2 80. f (x) = (3x2

2x + 5)4

4