Exercises

Exercises for Lecture #2

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Back to Examples #2

1-30. Find the partial derivatives and full differentials of the functions:

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

27. 28.

29. 30.

31-40. Find the derivatives of the composite functions:

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41-50. Find the gradient of functions in a given point:

41. 42.

43. 44.

45. 46.

47. 48.

49. 50.

51-60. Find the derivatives of functions in a given direction and at a given point:

51. , at the point M(3,2,1) in direction of a vector .

52. , at the point M(3,4) in direction of a gradient.

53. at the point M(1,2,3) in direction of a vector .

54. at the point M(3,1) in direction of a vector

55. at the point M(1,1) in direction of a bisector of the first coordinate corner.

56. at the point M(1,1,2) in direction of a vector which create 60°, 45°, 60° angles with the coordinate axises.

57. at the point M(5,1,2) in direction of a vector .

58. at the point M(1,1) in direction of a vector .

59. at the point M(2,1) in direction of a vector .

60. at the point M(3,4) in direction of a vector .