derivadas resueltas
Hallar las derivadas simplificadas de las siguientes funciones:
22. y=(x2+1)100
1.
y=3
(y’=0)
2.
y=x
(y’=1)
3.
y=5x
(y’=5)
4.
y=x(y’=1)
5.
y=x4+x3+x2+x+1
(y’=4x3+3x2+2x+1)
4
3
2
23. y =
3
6.
y= 4x -x +3x -7
7.
2
1
1
1
y = − x5 + 4x4 − x3 + x 2 − 3
5
6
2
(y’=16x -3x +6x)
1 2
⎛
⎞
43
⎜ y' = − x + 16x − x + x ⎟
2
⎝
⎠
8.
y=3(x2+x+1)
9.
y=4(3x3-2x2+5)+x2+1 (y’=36x2-14x)
(y’=3(2x+1))
x +1
x −1
24. y =
(y’=200 x (x2+1)99)
1
x2 + 1
25. y = 3
⎛−2 ⎞
⎜ y' =
⎟
⎜
(x − 1) 2 ⎟
⎝
⎠
⎛
− 2x ⎞
⎜ y' = 2
⎟
⎜
(x + 1) 2 ⎟
⎝
⎠
2x 2 − 1
3
x +1
4
⎛
44(2 x − 3) 3 ⎞
⎜ y' =
⎟
⎜
( x + 4) 5 ⎟
⎝ x+4 ⎠
⎝
⎠
2
⎛
x ⎞
27. y = x + 1
⎜y' =
⎟
⎜
⎟
x 2 +1 ⎠
⎝
4
3
2
28. y = 2 ⋅ x3 − x 2 + 1 ⋅ (2x 2 + 3) ⎛ y' = 14 x − 12 x + 9 x + 2 x ⎞
⎟
⎜
⎟
⎜
3
2
x − x +1
⎠
⎝
1
1 ⎞
⎛
29. y=log10x
⎜ y' = log10 e =
⎟
x
x ln10⎠
⎝
26. y = ⎛ 2x − 3 ⎞
⎜
⎟
30. y=ln x
(y’=1/x)
3
2
10. y = 2x − 3x + 4x − 5 (y’=3x2-3x+2)
2
31. y=3log2x- 4lnx
11. y=(x2+1) (2x3-4)
(y’=10x4+6x2-8x)
32. y=ln(3x2+4x+5)12. y=1/x
(y’= -1/x2)
13. y=1/x3
(y`= -3/x4)
5
33. y = ln x 2 − 1
34. y = ln(x2 − 1)
6
14. y=1/x
(y’= -5/x )
15. y = 2 + 1 − 3
x3 x 2 x
⎛
3x 2 − 2x − 6 ⎞
⎟
⎜ y' =
⎟⎜
x4
⎠
⎝
1 ⎞
⎛
⎜ y' =
⎟
2 x⎠
⎝
2 ⎞
⎛
⎜ y' = 3 ⎟
3⋅ x ⎠
⎝
16. y =
x
17. y = 3 x 2
18. y = x
5
3
⎛
3
⎜ y' =
⎜
5
5⋅ x2
⎝
⎞
⎟
⎟
⎠
⎛
− 2x 4 + 3x 2 + 4x ⎞
⎜y' = 3
⎟
⎜
⎟
(x 3 + 1) 2
⎝
⎠
35. y=2x
36. y = 2 x
2
37. y = e 2 x
⎛
⎞
x
⎜ y' =
⎟
⎜
(x2 − 1) ln(x2 − 1) ⎟
⎝
⎠
+ x +1
2
−3 x + 5
38. y=e-x
(y’= -1/ex)
39. y =e1 / x
40. y = 10
− 4 + 3log2e ⎞
⎛
⎜ y' =
⎟
x
⎝
⎠
6x + 4 ⎞
⎛
⎜ y' = 2
⎟
3x + 4x + 5 ⎠
⎝
x ⎞
⎛
⎜ y' = 2
⎟
x −1⎠
⎝
x
41. y=sen 2x
42. y=sen x2
19. y = 2 ⋅ 3 x 2 −...
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