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Publicado: 26 de febrero de 2013
UNIVERSIDAD INDUSTRIAL DE SANTANDER. SEDE BARRANCABERMEJA
ASIGNATURA: CÁLCULO I. GRUPO H1
TALLER DERIVADAS
Calcule las derivadas de las siguientes funciones
1. f (x ) = −
2. f (x ) =
cos x
4+ cot x
3
3sen x 3
(x
+ 1)
5
(x
4. f (x ) = cos 2
(x
3
2
(
4x + 1
3
34
5
(x
(x
− 2)
3
− 3)
2
6. f (x ) = ln x + 1 + x 2
x e +1
x ln x+ 1
e x cos x
8. f (x ) =
1 − senx
7. f (x ) =
9. f (x ) =
)
( sen 4x + tan 3x )
+ 1)
(
− 2)
− 3)
3. f (x ) = x arccos
5. f (x ) =
(x
34
3x
)
x⎞
⎟
⎝a ⎠a 2 − x 2 + a ⋅ arcsen ⎛
⎜
10. f (x ) =
x+ x+ x+ x
⎛a +x ⎞
11. f (x ) = arctan⎜
⎟
⎝ 1 − ax ⎠
ln (sen (x 2 + 1))
12. f (x ) =
x
13. xseny + ysenx = 0
14. f (x ) = ln (x 2 ln 4 (x ))15. f (x ) = tan (x 3 + ln (x 4 + 1))
1
1
+
.
x −1 x +1
2x
17. f (x ) =
x +3
16. y =
( (x
18. f (x ) = tan sen
Hallar y '''
2
+1
))
()
19. f (x ) = (3x + 5 ) x + 1cos x 2
x 3senx
tan x
x 3 + 5x 2 + 1
21. f (x ) =
x
22. f (x ) = ln[sen (x 2 + 5 )]
20. f (x ) =
23. f (x ) = (3x + 1)
2x
24. f (x ) = tan 4 x
1+x2
25. f (x ) = ln
1−x2
26. f(x ) = sen (senx )
27. f (x ) =
sen 5 x 2
28. f (x ) = e x tan x
29. f (x ) = x x +1
30. f (x ) = 2 arccos 2x + 1 − 4x 2
31. f (x ) = tan x −
x
cos 2 x
1
1
32. f (x ) =
+
2
sen xcos 2 x
33. f (x ) = cot 3 (3x + 1)
34. f (x ) = (5senx − 3 sec x )
3
35. f (x ) = ln (sen x )
36. f (x ) = sen 2 2t cos 2t
37.
x + y = 100
(
)
38. f (x ) = sen 3 sen 2 (senx)
x2 −x +1
x2 +x +1
1 + 2 tan x
40. f (x ) = ln
2 + tan x
x cos x
41. f (x ) = e
1 − cosh x
42. f (x ) =
1 + cosh x
43. f (x ) = senh (x 2 )
44. f (x ) = cos(ln x )
45. y = x ln x .Hallar y ''
d
1
(cosh −1 x ) = 2
46. Demuestre que:
dx
x −1
47. y = 2x + 3. Hallar y '''
48. x 2 y + xy 2 = 3x
tan x − 1
49. f (x ) =
sec x
1 + senx
50. f (x ) = ln
1 − senx
39. f (x )...
ASIGNATURA: CÁLCULO I. GRUPO H1
TALLER DERIVADAS
Calcule las derivadas de las siguientes funciones
1. f (x ) = −
2. f (x ) =
cos x
4+ cot x
3
3sen x 3
(x
+ 1)
5
(x
4. f (x ) = cos 2
(x
3
2
(
4x + 1
3
34
5
(x
(x
− 2)
3
− 3)
2
6. f (x ) = ln x + 1 + x 2
x e +1
x ln x+ 1
e x cos x
8. f (x ) =
1 − senx
7. f (x ) =
9. f (x ) =
)
( sen 4x + tan 3x )
+ 1)
(
− 2)
− 3)
3. f (x ) = x arccos
5. f (x ) =
(x
34
3x
)
x⎞
⎟
⎝a ⎠a 2 − x 2 + a ⋅ arcsen ⎛
⎜
10. f (x ) =
x+ x+ x+ x
⎛a +x ⎞
11. f (x ) = arctan⎜
⎟
⎝ 1 − ax ⎠
ln (sen (x 2 + 1))
12. f (x ) =
x
13. xseny + ysenx = 0
14. f (x ) = ln (x 2 ln 4 (x ))15. f (x ) = tan (x 3 + ln (x 4 + 1))
1
1
+
.
x −1 x +1
2x
17. f (x ) =
x +3
16. y =
( (x
18. f (x ) = tan sen
Hallar y '''
2
+1
))
()
19. f (x ) = (3x + 5 ) x + 1cos x 2
x 3senx
tan x
x 3 + 5x 2 + 1
21. f (x ) =
x
22. f (x ) = ln[sen (x 2 + 5 )]
20. f (x ) =
23. f (x ) = (3x + 1)
2x
24. f (x ) = tan 4 x
1+x2
25. f (x ) = ln
1−x2
26. f(x ) = sen (senx )
27. f (x ) =
sen 5 x 2
28. f (x ) = e x tan x
29. f (x ) = x x +1
30. f (x ) = 2 arccos 2x + 1 − 4x 2
31. f (x ) = tan x −
x
cos 2 x
1
1
32. f (x ) =
+
2
sen xcos 2 x
33. f (x ) = cot 3 (3x + 1)
34. f (x ) = (5senx − 3 sec x )
3
35. f (x ) = ln (sen x )
36. f (x ) = sen 2 2t cos 2t
37.
x + y = 100
(
)
38. f (x ) = sen 3 sen 2 (senx)
x2 −x +1
x2 +x +1
1 + 2 tan x
40. f (x ) = ln
2 + tan x
x cos x
41. f (x ) = e
1 − cosh x
42. f (x ) =
1 + cosh x
43. f (x ) = senh (x 2 )
44. f (x ) = cos(ln x )
45. y = x ln x .Hallar y ''
d
1
(cosh −1 x ) = 2
46. Demuestre que:
dx
x −1
47. y = 2x + 3. Hallar y '''
48. x 2 y + xy 2 = 3x
tan x − 1
49. f (x ) =
sec x
1 + senx
50. f (x ) = ln
1 − senx
39. f (x )...
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