1. Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Chapter 14 Partial Derivatives

3. Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 14.1 Functions and Several Variables

4. Slide 14 - 4 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

5. Slide 14 - 5 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

6. Slide 14 - 6 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

7. Slide 14 - 7 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

8. Slide 14 - 8 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

9. Slide 14 - 9 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

10. Slide 14 - 10 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

11. Slide 14 - 11 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

12. Slide 14 - 12 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

13. Slide 14 - 13 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

14. Slide 14 - 14 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

15. Slide 14 - 15 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

16. Slide 14 - 16 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

17. Slide 14 - 17 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

18. Slide 14 - 18 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

19. Slide 14 - 19 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

20. Slide 14 - 20 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

21. 14.2 Limits and Continuity in Higher Dimensions

22. Slide 14 - 22 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

23. Slide 14 - 23 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

24. Slide 14 - 24 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

25. Slide 14 - 25 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

26. Slide 14 - 26 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

27. Slide 14 - 27 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

28. Slide 14 - 28 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

29. Slide 14 - 29 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

30. Slide 14 - 30 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

31. Slide 14 - 31 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

32. Slide 14 - 32 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

33. 14.3 Partial Derivatives

34. Slide 14 - 34 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

35. Slide 14 - 35 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

36. Slide 14 - 36 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

37. Slide 14 - 37 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

38. Slide 14 - 38 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

39. Slide 14 - 39 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

40. Slide 14 - 40 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

41. Slide 14 - 41 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

42. Slide 14 - 42 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

43. Slide 14 - 43 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

44. Slide 14 - 44 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

45. Slide 14 - 45 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

46. Slide 14 - 46 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

47. Slide 14 - 47 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

48. Slide 14 - 48 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

49. Slide 14 - 49 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

50. Slide 14 - 50 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

51. 14.4 The Chain Rule

52. Slide 14 - 52 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

53. Slide 14 - 53 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

54. Slide 14 - 54 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

55. Slide 14 - 55 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

56. Slide 14 - 56 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

57. Slide 14 - 57 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

58. Slide 14 - 58 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

59. Slide 14 - 59 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

60. Slide 14 - 60 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

61. Slide 14 - 61 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

62. Slide 14 - 62 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

63. Slide 14 - 63 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

64. Slide 14 - 64 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

65. Slide 14 - 65 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

66. 14.5 Directional Derivatives and Gradient Vectors

67. Slide 14 - 67 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

68. Slide 14 - 68 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

69. Slide 14 - 69 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

70. Slide 14 - 70 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

71. Slide 14 - 71 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

72. Slide 14 - 72 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

73. Slide 14 - 73 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

74. Slide 14 - 74 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

75. Slide 14 - 75 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

76. Slide 14 - 76 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

77. Slide 14 - 77 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

78. Slide 14 - 78 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

79. Slide 14 - 79 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

80. Slide 14 - 80 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

81. Slide 14 - 81 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

82. 14.6 Tangent Planes and Differentials

83. Slide 14 - 83 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

84. Slide 14 - 84 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

85. Slide 14 - 85 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

86. Slide 14 - 86 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

87. Slide 14 - 87 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

88. Slide 14 - 88 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

89. Slide 14 - 89 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

90. Slide 14 - 90 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

91. Slide 14 - 91 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

92. Slide 14 - 92 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

93. Slide 14 - 93 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

94. Slide 14 - 94 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

95. Slide 14 - 95 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

96. Slide 14 - 96 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

97. Slide 14 - 97 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

98. 14.7 Extreme Values and Saddle Points

99. Slide 14 - 99 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

100. Slide 14 - 100 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

101. Slide 14 - 101 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

102. Slide 14 - 102 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

103. Slide 14 - 103 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

104. Slide 14 - 104 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

105. Slide 14 - 105 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

106. Slide 14 - 106 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

107. Slide 14 - 107 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

108. Slide 14 - 108 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

109. Slide 14 - 109 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

110. Slide 14 - 110 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

111. Slide 14 - 111 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

112. Slide 14 - 112 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

113. Slide 14 - 113 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

114. Slide 14 - 114 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

115. Slide 14 - 115 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

116. Slide 14 - 116 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

117. Slide 14 - 117 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

118. Slide 14 - 118 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

119. Slide 14 - 119 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

120. Slide 14 - 120 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

121. 14.8 Lagrange Multipliers

122. Slide 14 - 122 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

123. Slide 14 - 123 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

124. Slide 14 - 124 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

125. Slide 14 - 125 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

126. Slide 14 - 126 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

127. Slide 14 - 127 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

128. Slide 14 - 128 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

129. Slide 14 - 129 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

130. Slide 14 - 130 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

131. Slide 14 - 131 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

132. Slide 14 - 132 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

133. Slide 14 - 133 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

134. 14.9 Partial Derivatives with Constrained Variables

135. Slide 14 - 135 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

136. Slide 14 - 136 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

137. Slide 14 - 137 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

138. 14.10 Taylor’s Formula for Two Variables

139. Slide 14 - 139 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

140. Slide 14 - 140 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

141. Slide 14 - 141 Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley