Derivadas
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DERIVADAS Hallar la derivada de las siguientes funciones: 3 3 2 2 4 x + x − x−5 2 5 7
1.
f ( x) =
2.
f ( x ) = x ⋅ ( x + 2)
3.
f ( x ) = x 2 ⋅ (7 − 2 x )
4.
f ( x) = (2 x − 5) ⋅ (4 − 3 x)
5.
23. f ( x) =
2 x 3 − 3 x 2 − 2 x − 4 44. f ( x) = 1 − 3 x + (5 x − 2) 3 x 2 x 2 − 3x + 6 45. f ( x) =
x 2 − 3x 2x − 5
2x − 5x 2 + x 3 24. f ( x) = (2 x − 8) ⋅ (3x − 4)
46. f ( x ) = 3
f ( x) = (− x 4 − 2) ⋅ (5 x − 7 x 2 )
25. f ( x) = 25 x 4 − 1
47. f ( x) = 35 x + e x
6.
f ( x) = (3 x 4 − 3 x 2 + 5) 4
26. f ( x) = x 2 + x 3 − 2
48. f ( x) = 2 x −3 − 3 x −1
7.
f ( x) = (1 − 2 x + 3 x 2 − 4 x 3 ) 5
8.
f ( x) =
2x + 5 3
9.
f ( x) =
2 x−3
10. f ( x) =
27. f ( x) = 2 x + 3 x − 28. f ( x) = sen (5 x − 3) 29. f ( x) = cos 3 x
31. f ( x) = cos (4 − 9 x 2 )
1− x 32. f ( x) = 1+ x
12. f ( x) = 6 x 5 − 3 x 4
33. f ( x) = x ⋅ 3 x 2 − 1
13. f ( x) = (3 − 4 x − 5 x 2 ) 4
34. f ( x) = 3 Ln x
x8 x5 14. f ( x) = − 9 3
35. f ( x) = sen
) ( 3
x2 + 5 16. f ( x) = 2 x +6 x 4 − 3x 2 + 7 x 17. f ( x) = 2x + 5
)
3
1 sen 3 x
59. f ( x) = 3 2 x − 1
x2 +1 39. f ( x) = 2 x −1
60. f ( x) =
19. f ( x) = x
2 − 5x 41. f ( x) = Ln 4
22. f ( x) = 3 x − 3 − x
52. f ( x) = sen ( x 2 − 1) + cos 3 x
58. f ( x) = 3 Ln ( x 2 − 1)
38. f ( x) = Ln ( x + 7)
2
42. f ( x) = 3 x 5 43.
3
e x −1 57. f ( x) = sen x 2
21. f ( x) = x − 5
)
+4 3 5x − x 5
3
37. f ( x) = cos 5 3 x
4
(3x f ( x) =
56. f ( x) = (cos 2 x ) − e 2 x −1
36. f ( x) = 4 2 x
f ( x) = e (3 x
4
−5 x
)
)
1 − 3x + (5 x − 2) 3 x
54. f ( x) = sen (3 x 4 − 2 x)
3 x2
40. f ( x) = x ⋅ e x
1+ x 1− x
50. f ( x) =
55. f ( x) =
(2 x + 3) 3 18. f ( x) = (3 x 2 − 2 x + 6) 2
20. f ( x) =
) (
x 53. f ( x) = Ln x −1
2x − 3 11. f ( x) = 3− x
15. f ( x) = x 2 − 1 ⋅ 2 x 2 − 3 x + 2
(
49. f ( x) = x 2 + 2 ⋅ Ln x 2 + 2
51.
30. f ( x) = Ln (7 x + 2)
4 x2
(
1 x
5 x 2 −4 x
61. f ( x) =
2 + 3x 1+ x ex −1 ex +1
62. f ( x) = (3 x − 1) ⋅ 2 x −1 63. f ( x) = log 2 ( x 3 − 2 x + 1)
2
64. f ( x) = log
x x −1
1.
f ( x) =
2.
f ( x ) = x ⋅ ( x + 2)
3.
f ( x ) = x 2 ⋅ (7 − 2 x )
4.
f ( x) = (2 x − 5) ⋅ (4 − 3 x)
5.
23. f ( x) =
2 x 3 − 3 x 2 − 2 x − 4 44. f ( x) = 1 − 3 x + (5 x − 2) 3 x 2 x 2 − 3x + 6 45. f ( x) =
x 2 − 3x 2x − 5
2x − 5x 2 + x 3 24. f ( x) = (2 x − 8) ⋅ (3x − 4)
46. f ( x ) = 3
f ( x) = (− x 4 − 2) ⋅ (5 x − 7 x 2 )
25. f ( x) = 25 x 4 − 1
47. f ( x) = 35 x + e x
6.
f ( x) = (3 x 4 − 3 x 2 + 5) 4
26. f ( x) = x 2 + x 3 − 2
48. f ( x) = 2 x −3 − 3 x −1
7.
f ( x) = (1 − 2 x + 3 x 2 − 4 x 3 ) 5
8.
f ( x) =
2x + 5 3
9.
f ( x) =
2 x−3
10. f ( x) =
27. f ( x) = 2 x + 3 x − 28. f ( x) = sen (5 x − 3) 29. f ( x) = cos 3 x
31. f ( x) = cos (4 − 9 x 2 )
1− x 32. f ( x) = 1+ x
12. f ( x) = 6 x 5 − 3 x 4
33. f ( x) = x ⋅ 3 x 2 − 1
13. f ( x) = (3 − 4 x − 5 x 2 ) 4
34. f ( x) = 3 Ln x
x8 x5 14. f ( x) = − 9 3
35. f ( x) = sen
) ( 3
x2 + 5 16. f ( x) = 2 x +6 x 4 − 3x 2 + 7 x 17. f ( x) = 2x + 5
)
3
1 sen 3 x
59. f ( x) = 3 2 x − 1
x2 +1 39. f ( x) = 2 x −1
60. f ( x) =
19. f ( x) = x
2 − 5x 41. f ( x) = Ln 4
22. f ( x) = 3 x − 3 − x
52. f ( x) = sen ( x 2 − 1) + cos 3 x
58. f ( x) = 3 Ln ( x 2 − 1)
38. f ( x) = Ln ( x + 7)
2
42. f ( x) = 3 x 5 43.
3
e x −1 57. f ( x) = sen x 2
21. f ( x) = x − 5
)
+4 3 5x − x 5
3
37. f ( x) = cos 5 3 x
4
(3x f ( x) =
56. f ( x) = (cos 2 x ) − e 2 x −1
36. f ( x) = 4 2 x
f ( x) = e (3 x
4
−5 x
)
)
1 − 3x + (5 x − 2) 3 x
54. f ( x) = sen (3 x 4 − 2 x)
3 x2
40. f ( x) = x ⋅ e x
1+ x 1− x
50. f ( x) =
55. f ( x) =
(2 x + 3) 3 18. f ( x) = (3 x 2 − 2 x + 6) 2
20. f ( x) =
) (
x 53. f ( x) = Ln x −1
2x − 3 11. f ( x) = 3− x
15. f ( x) = x 2 − 1 ⋅ 2 x 2 − 3 x + 2
(
49. f ( x) = x 2 + 2 ⋅ Ln x 2 + 2
51.
30. f ( x) = Ln (7 x + 2)
4 x2
(
1 x
5 x 2 −4 x
61. f ( x) =
2 + 3x 1+ x ex −1 ex +1
62. f ( x) = (3 x − 1) ⋅ 2 x −1 63. f ( x) = log 2 ( x 3 − 2 x + 1)
2
64. f ( x) = log
x x −1
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