Ciencias

Derivada de las funciones elementales
1. f(x) = k
2.
3. k - k
4. f'(a) = lim ------- = 0
5. x->a x - a
6.
7. => f'(x) = 0
8.
9. f(x) = bx + c
10.11. bx + c - ba - c b(x - a)
12. f'(a) = lim --------------- = lim -------- = b
13. x->a x - a x->a x - a
14.
15. => f'(x) = b
16.
17. f(x) = xn
18.
19. xn- an
20. f'(a) = lim --------- =
21. x->a (x-a)
22.
23. (x - a)(xn-1 + axn-2 + a2xn-3 + ... + an-1)
24. lim ------------------------------------------ = nan-1
25. x->a (x-a)
26.
27. => f'(x) =nxn-1
28.
29. f(x) = bxn
30.
31. bxn - ban b(xn - an)
32. f'(a) = lim ---------- = lim ----------- = bnan-1
33. x->a x - a x->a x - a
34.
35. => f'(x) = bnxn-1
36.
37.f(x) = Lx equiv. a x/a - 1 (límites tipo)
38. --^--
39. Lx - La L(x/a) x - a 1
40. f'(a) = lim -------- = lim ------- = lim --------- = --
41. x->a x - a x->a x - a x->a a(x - a) a
42.
43.1
44. => f'(x) = ---
45. x
46.
47. f(x)=logcx
48. logcd = Ld/Lc
49. |
50. logcx - logca logc(x/a) | logc(x/a) 151. f'(a)=lim ------------- = lim ---------- = lim --------- = ---
52. x->a x - a | x->a (x - a) x->a Lc(x - a) aLc
53. |
54. log a - log b = log(a/b)
55.
56. 1
57.=> f'(x) = ---
58. xLc
59.
60. f(x) = ex
61. equiv. a 1 (límites tipo)
62. ---^---
63. ex - ea ea(ex-a - 1)
64. f'(a) = lim --------- = lim ------------ = ea65. x->a x - a x->a x - a
66.
67. => f'(x) = ex
68.
69. f(x) = bx
70. equiv. a (x-a)Lb (límites tipo)
71. ----^----
72. bx - ba ba(bx-a - 1)ba(x - a)Lb
73. f'(a)=lim ------- = lim ------------ = lim ----------- = baLb
74. x->a x - a x->a x - a x->a x - a
75.
76. => f'(x) = bxLb
77.
78. f(x) = sen x
79. equiv. a (x-a)/2 (límites tipo)
80....