Ejercicios de derivadas matematicas.

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  • Publicado : 11 de julio de 2010
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1. y=-10
y´=0
2. y=5
y´=0
3. f(x)=a2
y´=0
4. s(t)=b2
s´(t)=0
5. y=6x
y´=6
6. y= 34 x
y´= 34
7. f(x)=ax
f´(x)=a
8. s(t)=b2t
s´(t)=b2
9. f(x)=5x 2
f´(x)=52
10. y=axb
y´=ab
11. f(x)=x5
f´(x)=5x-4
12. f(x)=4x3
f´(x)=12x2
13. s(t)= 15t4
s´(t)= 45t3
14. y=x92
y´= 92 x 72
15. f(x)=x 43
f´(x)= 43x 13

16. y=6x 32
y´=9x 1217. f(x)=x 25
f´(x)= 25x -35
f´(x)= 25x 35
f´(x)= 25x 3
18. f(x)=4x 14
f´(x)= 44 x -3 4
f´(x)= x -3 4
f´(x)= 1x 3 4
f´(x)= 1 4x3
19. f(x)= x
f´(x)= 12x
f´(x)= 1 2x
20. s(t)= 4t
s´(t)= 14t 14
s´(t)= 14t -34
s´(t)= 14 t 34
s´(t)= 14 4t 3
21. f(x)=5 5x
f´(x)= 15x 15
f´(x)=x-4 5
f´(x)= 1x45
f´(x)= 15x 4
22. f(x)= x 57
f´(x)= 5x 4 7
23. f(x)= x 49f´(x)= 4x 39

24. s(t)= t 3a
s´(t)= 3t 2a
25. f(x)= 5x 4
f´(x)=5x4
f´(x)=20x3
f´(x)= 20x3
26. f(x)= 2x6
f´(x)=2x7
f´(x)= 12x6
f´(x)= 12x 7
27. f(x)= x2
f´(x)= x 122
f´(x)=x12+2
f´(x)= 12x+2
f´(x)= 14x
f´(x)= 14 x
28. s(t)= 3t5
s´(t)= 13t5
s´(t)= 13 t 13-5
s´(t)=15t
s´(t)= 1153t 2
29. f(x)= 4x
f(x)=4x-12
f´(x)= 42 x -12
f´(x)= 42x22
f´(x)= 42xx 3f´(x)= 2x 3
f´(x)= 2xx

30. s(t)= 54t
s(t)= 5 14 t -14
s´(t)= 54t4t
31. f(x)= 43x
f´(x)= 4 13x-13
f´(x)= 43x3x
32. f(x)=7x3-3x2+3x-12
f´(x)=21x2-6x+3
33. f(x)=x4-5x3+8x2-x-6
f´(x)=4x3-15x2+16x-x
34. f(x)=5x2+4x+amn-2
f(x)=10x+4
35. f(x)=3ax4-4ax3+ 5bx2+7cx
f´(x)=12ax3-12ax2-10bx+7c
36. f(x)= x 36 – 3x 25 - 4x9 - 15
f´(x)= x 26¿2 – 6x5 - 49
37. s(t)=t 36 – t 4 5 – t 34 - t 27 + t9 – 23
s´(t)= 5t 46 – 4t 3 5 – 3t 24 - 2t7 + 19
38. f(x)= x 2a 2+b 2 - xa + cb
f´(x)= 2xa2+b2 - 1a
39. s(t)= 4t2 - 5t - 95
s´(t)= 8t3 - 5t2
40. f(x)= 5x4 – 6x3 – 7x2 – 4t2 – 3x + 35
f´(x)=- 20x5 + 18x4 + 14x3 + 3x2
41. s(x)= t35 - 2t2 - 6t - 35
s´(x)= 3t25 - 4t3 - 6t2
42. f(x)= 3x5 - 33x
f´(x)= 115 3x2 + 1x 3x
43. f(x)=x4-3x3-6x2-3x+2x
f´(x)=-3x2-6x-6-2x2
44. dydx y= 1(4x2+6x-7)3
y=(4x2+6x-7)3
dydx= dx(4x2+6x-7)-3
=-3(4x2+6x-7)-4
=8x+6
=-6(4x+3)(4x2+6x-7)4
45. f(x)=3x2-5x+4
f´(x)=lim 3x+h2 -5x+h+4-(3x2-5x+4)h
h 0
=lim 3x2+6xh+3h2-5x-5h+4-(3x2-5x+4)h
=lim 6xh+3h2-5hh
=lim (6x+3h-5)
=6x-5
46. y=2x+5
y´=2
47. y=5
y´=0
48. 3c
y´=0
49. y= 6
y´=0
50. y=5x
y´=5
51. y= 52 xy´= 52
52. y=2+ x2
y=2+ 12 x
y´= 12
53. y= -2x+17
y= -27 x+1
y´= -27
54. y=3x2-x+5
y=3x2-x+5
y´=2(3x)2-1-1+0
y´=2(3x)-1
y´=6x-1
55. y= 3x7 -c2
y´= 37
56. y=x2-5x-3
y´=2x-5
57. y=(4-x)(3x+x)
y´=(4-x)(1)+(3+x)(-1)
y´=(4-x)+(-3-x)
y´=4-x-3-x
y´=1-2x
58. y=(x2-x)(x-4)
y´=(x2-x)(1)+(x-4)(2x-1)
y´=x2-x+2x2-x-8x+4
y´=3x2-10x+4

59. y=(3-x)(2-x)(5-x)y=30-31x+10x2-x3
y´=-31+20x-3x2
60. y=9(x-1)(2x+3)
y=18x2+9x-27
y´=-31+20x-3x2
61. y=3x5
y´=15x4
62. y=ax4
y´=4ax3
63. y=3x 13
y´=x-23
64. y=3x2-6x+5
y´=6x-6
65. y=2x-7
y´=2
66. y=3x + 23x 2
y=13x + 2x23
y=13x + 2x - 23
y´=13 - 43x 53
y´=13 - 43 3x 5
67. y=1x - 4x 3
y=x-1-x34
y´=x-2 - 34x -14
y´=1x2 - 34x14
y´=1x2 - 34 4x
68. y=x-25
y=x5 - 25y=15 x - 25
y´=15

69. y= 5x24x
y=54 x
y´=54
70. y=ax5b
y=ab x5
y´=5ab x4
71. y=x na
y=1a xn
y´=na xn-1
72. y=x
y=x12
y´=12x-12
y´=12x12
y´=12x
73. y=3x2
y=x23
y´=23x-23
y´=23x23
74. 45x2 + 23x3 -3
y=45x2 + 23x3 -3
y=4x-25 + 2x-33 -3
y´=-85 x-3 - 63 x-4
y´= - 85x3 - 2x4
75. y=35 x5
y=155 x4
y´=3x4
76. y=5x3
y´=25 x-25
y´=35x 25
y´=355x277. y=5x4
y´=20x-5
y´=-20x5
78. y=2x3+3x4
y´=64x2 + 34
y´=32x2 + 34
79. y=3x + 23x2
y=3x + 223x4
y=x-3 + 2123x
y=x-3+6x+3
y´=x-3+6
80. y=x2 - 23x3 + 3x
y=x22 - 2x33 + 3x12
y=x- 2x +3x12
y=x-2x+3x-12
y´=1+2x2 - 222x3
81. y=(3x+5)2
y=9x2+15x+15x+25
y=9x2+30x+25
y=18x+30
dydx y=(2u)(3)
= 6u
dydx =6(3x+5)

82. y=2x3+5
y=(2x3+5) 12
y=u 12
y´= 12 u-...
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