1
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Các hàm vi phân x và y liên hệ với nhau

2
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bời phương trình sau.

3
00:00:05,965 --> 00:00:08,715
sin x cộng cosin y

4
00:00:09,578 --> 00:00:12,479
bằng căn bậc hai của 2.

5
00:00:12,479 --> 00:00:15,128
Đề còn cho mình biết đạo hàm của x

6
00:00:15,128 --> 00:00:17,897
theo t bằng 5.

7
00:00:17,897 --> 00:00:21,530
Đề hỏi mình tìm đạo hàm của y

8
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theo t khi y bằng pi trên 4

9
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và 0 nhỏ hơn x nhỏ hơn pi trên 2.

10
00:00:29,789 --> 00:00:32,365
Vậy đề cho mình biết đạo hàm

11
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của x theo t và nói mình tìm

12
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đạo hàm của y theo t,

13
00:00:37,134 --> 00:00:41,301
vậy mình có thể xem x và y là các hàm theo t.

14
00:00:42,403 --> 00:00:45,751
Vậy mình có thể viết lại phương trình ngay đây.

15
00:00:45,751 --> 00:00:48,584
Mình có thể viết nó thành sin x,

16
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một hàm theo t,

17
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cộng cosin

18
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của y, một hàm cũng theo t,

19
00:00:59,499 --> 00:01:02,082
bằng căn bậc hai của 2.

20
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Bây giờ mình có thể thấy hơi bối rối,

21
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mình không quen coi x như một hàm

22
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theo một biến thứ ba hay y như một hàm

23
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theo một cái gì đó khác x.

24
00:01:10,068 --> 00:01:11,740
Nhưng nhớ là x và y là các biến số.

25
00:01:11,740 --> 00:01:15,419
Cái này có thể là f(t) và cái này có thể là g(t)

26
00:01:15,419 --> 00:01:17,605
thay vì x theo t hay y theo t,

27
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và cái đó có thể thấy quen thuộc hơn.

28
00:01:19,503 --> 00:01:23,170
Nhưng dù gì, nếu mình muốn tìm dy dt,

29
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điều mình muốn làm là lấy đạo hàm

30
00:01:26,264 --> 00:01:29,952
theo t ở cả 2 vế phương trình.

31
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Vậy hãy làm vậy.

32
00:01:31,357 --> 00:01:33,303
Mình sẽ làm vế trái trước,

33
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vậy mình sẽ lấy đạo hàm cái này theo t,

34
00:01:36,541 --> 00:01:38,035
và lấy đạo hàm cái này theo t.

35
00:01:38,035 --> 00:01:41,001
Mình sẽ lấy đạo hàm hai cái đó theo t.

36
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Và rồi mình sẽ lấy đạo hàm

37
00:01:42,338 --> 00:01:46,547
của vế phải, hằng số này theo t.

38
00:01:46,547 --> 00:01:49,764
Vậy hãy xem mấy cái này.

39
00:01:49,764 --> 00:01:51,444
Cái này là gì đây?

40
00:01:51,444 --> 00:01:53,114
Để mình dùng màu khác.

41
00:01:53,114 --> 00:01:56,622
Vậy cái

42
00:01:56,622 --> 00:01:58,245
0:01:58.245,0:02:00.405

43
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0:02:04.918,0:02:07.768

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0:02:13.817,0:02:14.650

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0:02:18.714,0:02:20.881

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0:02:22.365,0:02:25.244

47
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0:02:28.766,0:02:32.780

48
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0:02:34.506,0:02:36.682

49
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0:02:38.737,0:02:41.272

50
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0:02:43.565,0:02:46.547

51
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0:02:48.503,0:02:51.415

52
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0:02:53.927,0:02:56.010

53
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0:03:01.216,0:03:04.327

54
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0:03:07.692,0:03:09.206

55
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0:03:14.264,0:03:17.447

56
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0:03:20.742,0:03:22.162

57
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0:03:23.912,0:03:27.385

58
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0:03:29.632,0:03:31.357

59
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0:03:33.681,0:03:38.277

60
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0:03:40.270,0:03:42.207

61
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0:03:44.964,0:03:47.157

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0:03:51.010,0:03:52.445

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0:03:54.467,0:03:58.372

64
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65
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66
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0:04:16.062,0:04:18.743

67
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0:04:21.785,0:04:25.398

68
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0:04:29.088,0:04:32.679

69
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0:04:36.145,0:04:40.312

70
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73
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0:05:00.222,0:05:03.754

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0:05:32.852,0:05:37.709

81
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0:05:39.469,0:05:40.764

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0:05:42.223,0:05:44.709

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0:05:48.718,0:05:50.768

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87
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89
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90
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91
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102
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103
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