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Nguyễn Minh Tiến – maths287
ĐẠO HÀM CÁC HÀM CƠ BẢN
-------maths287------BẢNG ĐẠO HÀM CÁC HÀM SƠ CẤP
y = c → y' = ( c) ' = 0
y = tan x → y ' = ( tan x ) ' =
y = x → y ' = ( x) ' = 1
y = cot x → y ' = ( cot x ) ' = −
( )
y = x n → y ' = x n ' = nx n−1
y = x → y' =
y=
1
cos 2 x
1
sin 2 x
y = k.u ( x ) → y ' = k.u ' ( x )
( x ) ' = 2 1x
y = u.v → y ' = ( u.v ) ' = u ' v + uv '
1
1
1
→ y ' = ÷' = − 2
x
x
x
y = sin x → y ' = ( sin x ) ' = cos x
y = cos x → y ' = ( cos x ) ' = − sin x
y=
1
1
1
→ y ' = ÷' = − 2
u
u
u
y=
u
u u ' v − uv '
→ y ' = ÷' =
v
v2
v
BÀI TẬP ÁP DỤNG
Tính đạo hàm các hàm số sau
1. y = x 3 − 2 x 2 + 3 x + 4 → y ' = ……………….....................................
2.
y = x 4 + 2 x → y ' = ………………………………………….
3.
y = − x 3 + 3x 2 − 4 x + 1 → y ' = ………………………………………….
4.
y = x − 2 x → y ' = ………………………………………….
5.
y=
7.
2x − 1
→ y ' = ………………………………………….
x+2
x 2 + 3x − 1
y=
→ y ' = ………………………………………….
x+1
y = x 4 + 3x 2 + 2 → y ' = ………………………………………….
8.
y=
6.
9.
x2
→ y ' = ………………………………………….
x −1
y = x 3 − 3x 2 → y ' = ………………………………………….
1
Nguyễn Minh Tiến – maths287
10. y = 4 x 3 − 12 x 2 + 9 x − 1 → y ' = .........................................
x2 + 2x + 2
→ y ' = ........................................
x+1
x 2 + 3x + 3
12. y =
→ y ' = ........................................
x+1
x4
5
13. y =
− 3 x 2 + → y ' = ........................................
2
2
4
2
14. y = − x − 2 x + 3 → y ' = ........................................
11. y =
x2 + x + 2
→ y ' = ........................................
x −1
2x2 + x
y=
→ y ' = ........................................
x+1
x2 + x + 1
y=
→ y ' = ........................................
x+1
x2 − 2x + 2
y=
→ y ' = ........................................
x −1
x 2 − 3x
y=
→ y ' = ........................................
x −1
1
7x
y = x4 − x5 +
→ y ' = ........................................
2
6
−3x 2 − x + 1
y=
→ y ' = ........................................
2x + 1
x2
y=
→ y ' = ........................................
x +1
2x2 + 2
y=
→ y ' = ........................................
−x + 1
y = sin x − cos x + tan x → y ' = ........................................
15. y =
16.
17.
18.
19.
20.
21.
22.
23.
24.
(
)
2
25. y = x + 1 ( 2 x − 1) → y ' = ........................................
(
)
2
26. y = + 3x ÷ x − 1 → y ' = ........................................
x
1
− 1 ÷ → y ' = ........................................
27. y = x + 1
x
28.
(
y=(
(
3
)
x + 2) ( 1 +
)(
3
)
x 2 + 3 x → y ' = ........................................
)(
)
2
2
2
29. y = x − 1 x − 4 x − 9 → y ' = ........................................
2
Nguyễn Minh Tiến – maths287
1+ x
30. y =
→ y ' = ........................................
1 + 2x
3
2
31. y = 2 − x + x x → y ' = ........................................
3
x
(
)
2
32. y = x + 3x ( 2 − x ) → y ' = ........................................
1 + x − x2
→ y ' = ........................................
1 − x + x2
34. y = ( 2 x + 1) sin x → y ' = .............................................
33. y =
3
1
7
2
2
35. y = x − x + 2 x + 3 x − x + ÷→ y ' = ............................................
2
6
x3 + x + 1
→ y ' = ............................................
36. y = 2
x −x−2
x4 + x3 + x − 1
→ y ' = ............................................
37. y =
x4 + 1
1
x2 + 1
− 2 → y ' = ............................................
38. y = 2
x −1
x
1
1
+
→ y ' = ............................................
39. y =
sin x cos x
x
→ y ' = ............................................
40. y =
1 − cos x
sin x
→ y ' = ............................................
41. y =
1 + cos x
3
2
42. y = x x − 4 → y ' = ............................................
(
)
(
)
2
43. y = ( x − 3 ) 1 − ÷ → y ' = ............................................
x
(
)
2
44. y = x + x + 1 ( 1 − sin x ) → y ' = ............................................
45. y = ( tan x + 1) ( sin x − cos x + 2 ) → y ' = ............................................
(
)
2
46. y = x 2 x − 1 → y ' = ............................................
47. y =
(
x +2
)(
(
1
48. y = x −
÷
x
49. y =
(
)
x + x 2 − 2 → y ' = ............................................
)
x + 2 x → y ' = ............................................
)
x + 2 ( sin x + 1 + x ) → y ' = ............................................
3
Nguyễn Minh Tiến – maths287
50. y = ( tan x + 2 )
(
(
)
x − 2 → y ' = ............................................
)
2
51. y = x − sin x ( tan x − 2 x ) → y ' = ............................................
x2 + 2x + 1
→ y ' = ............................................
x − 3x2
x 2 + 3x + 3
→ y ' = ............................................
53. y = 2
x − 3x − 3
52. y =
x −2
54. y =
x +3
3x − 1
55. y =
56. y =
57. y =
→ y ' = ............................................
x− x
x+ x
1
→ y ' = ............................................
x2 + x
(
58. y = 3 − 2 x 2
59.
→ y ' = ............................................
5x + 2
( x + 2)
y=
→ y ' = ............................................
)
2
→ y ' = ............................................
2
→ y ' = ............................................
x −1
60. y = x6 − 2 x + 2 x 2 → y ' = ............................................
1
3
− x + → y ' = ............................................
x+2
x
5
− x + 5x → y ' = ............................................
62. y = 2
x −1
61. y =
63. y = x . ( sin x − cos x ) → y ' = ............................................
)(
(
)
2
64. y = x − 3x + 2 tan x − x → y ' = ............................................
65. y =
66. y =
67. y =
4
cos x
x
→ y ' = ............................................
x + x −1
x −x+1
→ y ' = ............................................
x− x +2
→ y ' = ............................................
x+2
