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Implicit Differentiation

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Uploaded on Jun 7, 2008

Taking the derivative when y is defined implicitly.

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Calculus

  1. 1

    Newton Leibniz and Usain Bolt

  2. 2

    Introduction to Limits (HD)

  3. 3

    Introduction to Limits

  4. 4

    Limit Examples (part 1)

  5. 5

    Limit Examples (part 2)

  6. 6

    Limit Examples (part3)

  7. 7

    Limit Examples w/ brain malfunction on first prob (part 4)

  8. 8

    Squeeze Theorem

  9. 9

    Proof: lim (sin x)/x

  10. 10

    More Limits

  11. 11

    Epsilon Delta Limit Definition 1

  12. 12

    Epsilon Delta Limit Definition 2

  13. 13

    Calculus: Derivatives 1 (new HD version)

  14. 14

    Calculus: Derivatives 2 (new HD version)

  15. 15

    Calculus: Derivatives 2.5 (new HD version)

  16. 16

    Derivative Intuition Module

  17. 17

    Calculus: Derivatives 1

  18. 18

    Calculus: Derivatives 2

  19. 19

    Calculus: Derivatives 3

  20. 20

    The Chain Rule

  21. 21

    Chain Rule Examples

  22. 22

    Even More Chain Rule

  23. 23

    Product Rule

  24. 24

    Quotient Rule

  25. 25

    Derivatives (part 9)

  26. 26

    Proof: d/dx(x^n)

  27. 27

    Proof: d/dx(sqrt(x))

  28. 28

    Proof: d/dx(ln x) = 1/x

  29. 29

    Proof: d/dx(e^x) = e^x

  30. 30

    Proofs of Derivatives of Ln(x) and e^x

  31. 31

    Extreme Derivative Word Problem (advanced)

  32. Implicit Differentiation

  33. 33

    Implicit Differentiation (part 2)

  34. 34

    More implicit differentiation

  35. 35

    More chain rule and implicit differentiation intuition

  36. 36

    Trig Implicit Differentiation Example

  37. 37

    Calculus: Derivative of x^(x^x)

  38. 38

    Introduction to L'Hopital's Rule

  39. 39

    L'Hopital's Rule Example 1

  40. 40

    L'Hopital's Rule Example 2

  41. 41

    L'Hopital's Rule Example 3

  42. 42

    Maxima Minima Slope Intuition

  43. 43

    Inflection Points and Concavity Intuition

  44. 44

    Monotonicity Theorem

  45. 45

    Calculus: Maximum and minimum values on an interval

  46. 46

    Calculus: Graphing Using Derivatives

  47. 47

    Calculus Graphing with Derivatives Example

  48. 48

    Graphing with Calculus

  49. 49

    Optimization with Calculus 1

  50. 50

    Optimization with Calculus 2

  51. 51

    Optimization with Calculus 3

  52. 52

    Optimization Example 4

  53. 53

    Introduction to rate-of-change problems

  54. 54

    Equation of a tangent line

  55. 55

    Rates-of-change (part 2)

  56. 56

    Ladder rate-of-change problem

  57. 57

    Mean Value Theorem

  58. 58

    The Indefinite Integral or Anti-derivative

  59. 59

    Indefinite integrals (part II)

  60. 60

    Indefinite Integration (part III)

  61. 61

    Indefinite Integration (part IV)

  62. 62

    Indefinite Integration (part V)

  63. 63

    Integration by Parts (part 6 of Indefinite Integration)

  64. 64

    Indefinite Integration (part 7)

  65. 65

    Another u-subsitution example

  66. 66

    Introduction to definite integrals

  67. 67

    Definite integrals (part II)

  68. 68

    Definite Integrals (area under a curve) (part III)

  69. 69

    Definite Integrals (part 4)

  70. 70

    Definite Integrals (part 5)

  71. 71

    Definite integral with substitution

  72. 72

    Integrals: Trig Substitution 1

  73. 73

    Integrals: Trig Substitution 2

  74. 74

    Integrals: Trig Substitution 3 (long problem)

  75. 75

    Periodic Definite Integral

  76. 76

    Simple Differential Equations

  77. 77

    Solid of Revolution (part 1)

  78. 78

    Solid of Revolution (part 2)

  79. 79

    Solid of Revolution (part 3)

  80. 80

    Solid of Revolution (part 4)

  81. 81

    Solid of Revolution (part 5)

  82. 82

    Solid of Revolution (part 6)

  83. 83

    Solid of Revolution (part 7)

  84. 84

    Solid of Revolution (part 8)

  85. 85

    Sequences and Series (part 1)

  86. 86

    Sequences and series (part 2)

  87. 87

    Maclauren and Taylor Series Intuition

  88. 88

    Cosine Taylor Series at 0 (Maclaurin)

  89. 89

    Sine Taylor Series at 0 (Maclaurin)

  90. 90

    Taylor Series at 0 (Maclaurin) for e to the x

  91. 91

    Euler's Formula and Euler's Identity

  92. 92

    Visualizing Taylor Series Approximations

  93. 93

    Generalized Taylor Series Approximation

  94. 94

    Visualizing Taylor Series for e^x

  95. 95

    Polynomial approximation of functions (part 1)

  96. 96

    Polynomial approximation of functions (part 2)

  97. 97

    Approximating functions with polynomials (part 3)

  98. 98

    Polynomial approximation of functions (part 4)

  99. 99

    Polynomial approximations of functions (part 5)

  100. 100

    Polynomial approximation of functions (part 6)

  101. 101

    Polynomial approximation of functions (part 7)

  102. 102

    Taylor Polynomials

  103. 103

    Exponential Growth

  104. 104

    AP Calculus BC Exams: 2008 1 a

  105. 105

    AP Calculus BC Exams: 2008 1 b&c

  106. 106

    AP Calculus BC Exams: 2008 1 c&d

  107. 107

    AP Calculus BC Exams: 2008 1 d

  108. 108

    Calculus BC 2008 2 a

  109. 109

    Calculus BC 2008 2 b &c

  110. 110

    Calculus BC 2008 2d

  111. 111

    Partial Derivatives

  112. 112

    Partial Derivatives 2

  113. 113

    Gradient 1

  114. 114

    Gradient of a scalar field

  115. 115

    Divergence 1

  116. 116

    Divergence 2

  117. 117

    Divergence 3

  118. 118

    Curl 1

  119. 119

    Curl 2

  120. 120

    Curl 3

  121. 121

    Double Integral 1

  122. 122

    Double Integrals 2

  123. 123

    Double Integrals 3

  124. 124

    Double Integrals 4

  125. 125

    Double Integrals 5

  126. 126

    Double Integrals 6

  127. 127

    Triple Integrals 1

  128. 128

    Triple Integrals 2

  129. 129

    Triple Integrals 3

  130. 130

    (2^ln x)/x Antiderivative Example

  131. 131

    Introduction to the Line Integral

  132. 132

    Line Integral Example 1

  133. 133

    Line Integral Example 2 (part 1)

  134. 134

    Line Integral Example 2 (part 2)

  135. 135

    Position Vector Valued Functions

  136. 136

    Derivative of a position vector valued function

  137. 137

    Differential of a vector valued function

  138. 138

    Vector valued function derivative example

  139. 139

    Line Integrals and Vector Fields

  140. 140

    Using a line integral to find the work done by a vector field example

  141. 141

    Parametrization of a Reverse Path

  142. 142

    Scalar Field Line Integral Independent of Path Direction

  143. 143

    Vector Field Line Integrals Dependent on Path Direction

  144. 144

    Path Independence for Line Integrals

  145. 145

    Closed Curve Line Integrals of Conservative Vector Fields

  146. 146

    Example of Closed Line Integral of Conservative Field

  147. 147

    Second Example of Line Integral of Conservative Vector Field

  148. 148

    Green's Theorem Proof Part 1

  149. 149

    Green's Theorem Proof (part 2)

  150. 150

    Green's Theorem Example 1

  151. 151

    Green's Theorem Example 2

  152. 152

    Introduction to Parametrizing a Surface with Two Parameters

  153. 153

    Determining a Position Vector-Valued Function for a Parametrization of Two Parameters

  154. 154

    Partial Derivatives of Vector-Valued Functions

  155. 155

    Introduction to the Surface Integral

  156. 156

    Example of calculating a surface integral part 1

  157. 157

    Example of calculating a surface integral part 2

  158. 158

    Example of calculating a surface integral part 3

  159. 159

    2011 Calculus AB Free Response #1a

  160. 160

    2011 Calculus AB Free Response #1 parts b c d

  161. 161

    2011 Calculus AB Free Response #2 (a & b)

  162. 162

    2011 Calculus AB Free Response #2 (c & d)

  163. 163

    2011 Calculus AB Free Response #3 (a & b)

  164. 164

    2011 Calculus AB Free Response #3 (c)

  165. 165

    2011 Calculus AB Free Response #4a

  166. 166

    2011 Calculus AB Free Response #4b

  167. 167

    2011 Calculus AB Free Response #4c

  168. 168

    2011 Calculus AB Free Response #4d

  169. 169

    2011 Calculus AB Free Response #5a

  170. 170

    2011 Calculus AB Free Response #5b

  171. 171

    2011 Calculus AB Free Response #5c.

  172. 172

    2011 Calculus AB Free Response #6a

  173. 173

    2011 Calculus AB Free Response #6b

  174. 174

    2011 Calculus AB Free Response #6c

  175. 175

    2011 Calculus BC Free Response #1a

  176. 176

    2011 Calculus BC Free Response #1 (b & c)

  177. 177

    2011 Calculus BC Free Response #1d

  178. 178

    2011 Calculus BC Free Response #3a

  179. 179

    2011 Calculus BC Free Response #3 (b & c)

  180. 180

    2011 Calculus BC Free Response #6a

  181. 181

    2011 Calculus BC Free Response #6b

  182. 182

    2011 Calculus BC Free Response #6c

  183. 183

    Error or Remainder of a Taylor Polynomial Approximation

  184. 184

    Proof: Bounding the Error or Remainder of a Taylor Polynomial Approximation

  185. 185

    2011 Calculus BC Free Response #6d

  186. 186

    Constructing a unit normal vector to a curve

  187. 187

    2 D Divergence Theorem

  188. 188

    Conceptual clarification for 2-D Divergence Theorem

  189. 189

    Surface Integral Example Part 2 - Calculating the Surface Differential

  190. 190

    Surface Integral Example Part 1 - Parameterizing the Unit Sphere

  191. 191

    Surface Integral Example Part 3 - The Home Stretch

  192. 192

    Surface Integral Ex2 part 1 - Parameterizing the Surface

  193. 193

    Surface Integral Ex2 part 2 - Evaluating Integral

  194. 194

    Surface Integral Ex3 part 1 - Parameterizing the Outside Surface

  195. 195

    Surface Integral Ex3 part 2 - Evaluating the Outside Surface

  196. 196

    Surface Integral Ex3 part 3 - Top surface

  197. 197

    Surface Integral Ex3 part 4 - Home Stretch

  198. 198

    Conceputal Understanding of Flux in Three Dimensions

  199. 199

    Constructing a unit normal vector to a surface

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