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EJERCICIOS DE DERIVADAS Calcular la derivada de las siguientes funciones:

1. f ( x ) = x 2 2. f ( x ) =
1 2x

16. f ( x ) =

1 3 2 + 2 + 3 x x x

17. f ( x ) = ( x 2 + 4) 2 (2 x 3 − 1) 318. f ( x ) = 3 3x 2 −
1 5x

3. f ( x ) = x 4. f ( x ) = 3x − 2 x + 1
2

19. f ( x ) = x 2 + 6 x + 3 5. f ( x ) = x 2 + x + 2 6. f ( x ) =
x 2 x +1

20. f ( x ) =

x2 4 − x2

7. f ( x ) = x+ 3 x , x > 0 8. f ( x ) =
x 1+ x

21. f ( x ) = sen (3x ) + cos(2 x ) 22. f ( x ) = tagx 2 23. f ( x ) = cos( x + 3) cos( x − 3) 24. f ( x ) =
senx x

9. f ( x ) = x 1 + x 2 10. f ( x ) =

x1− x2

, −1 < x < 1

25. f ( x ) = sen ( x 2 − 2 x ) 26. f ( x ) = sen 3 4 x 27. f ( x ) = (1 − cos 2 x ) 3 28. f ( x ) = cos(cos x ) 29. f ( x ) = 3 tag 2x 30. f ( x ) = x arctgx 31. f ( x ) =arcsen 1 − x 2 32. f ( x ) = (1 + cos 3 x ) 4

1− x 11. f ( x ) = 1+ x
12. f ( x ) = x 9 − x 2 13. f ( x ) = 3 x 2 + 2 x + 2 14. f ( x ) =
3x 2 + 5 ( x − 1)( x − 2)

3 − 2x 15. f ( x ) = 3 + 2x 33. f ( x ) = sen 3 ( x 2 − 1) tag 1 − 2 x 34. f ( x ) =
1− x2 x cos 3 2 1− x 1+ x 1 x

51. f ( x ) =

x ex

52. f ( x ) = x 2 e x 53. f ( x ) = e
s

35. f ( x ) = arctg

54. f ( x ) =e x + e −x e x − e −x
2

36. f ( x ) = arctg x 2 − 1 + arcsen
x x +1
2

55. f ( x ) = ln(senx cos x ) + xe − x 56. f ( x ) = ln(5e x −1 ) ( x + 3x 2 ) 3 57. f ( x ) = ln[arctg(senx ) ] 58. f( x ) = e 2 cos
2

37. f ( x ) = sen

38. f ( x ) = e x − x − 1 39. f ( x ) = xe 3x 40. f ( x ) = ln(1 + x 2 ) 41. f ( x ) =
ln x x

3x

59. f ( x ) = tag 2 ( x + e x ) 60. f ( x ) =
e 2x+ 1 sen 3 5x

42. f ( x ) = x 2 e − x 43. f ( x ) = ln( x + x 2 + 1) 44. f ( x ) = x ln( x 2 + 1) 45. f ( x ) = 4sen 2 (2 x ) ln( x 2 − 1) 46. f ( x ) =
2 cos 3 (− x 3 + 4) ln( x 4 + x − 3)
247. f ( x ) = e x

+7x

+2

48. f ( x ) = ln( x 2 − 3x ) cos(1 / x ) 49. f ( x ) = ln(sen 2 x ) + x 2 e − x 50. f ( x ) = ln x 2 + ln x

FUNCIÓN
y=a y = af(x) y = f(x)+g(x) y = f(x)-g(x) y...
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