Udemy, Coursera, 2U/edX Face Lawsuits Over Meta Pixel Use

Introduction to Differentiation

Introduction to Differentiation

Eddie Woo via YouTube Direct link

Where does the Product Rule come from? (2 of 2: Derivation)

55 of 113
Previous
Next

55 of 113

Where does the Product Rule come from? (2 of 2: Derivation)

Class Central Classrooms beta

YouTube playlists curated by Class Central.

Classroom Contents

Introduction to Differentiation

Automatically move to the next video in the Classroom when playback concludes
  1. 1 Prologue to Calculus (1 of 5: How fast did Usain Bolt run?)
  2. 2 Prologue to Calculus (2 of 5: How can we measure more accurately?)
  3. 3 Prologue to Calculus (3 of 5: The difference quotient)
  4. 4 Prologue to Calculus (4 of 5: Exploring a parabola)
  5. 5 Prologue to Calculus (5 of 5: Gradient of the tangent)
  6. 6 Basics of Calculus (1 of 5: Foundational language & notation)
  7. 7 Basics of Calculus (2 of 5: Example of using first principles)
  8. 8 Basics of Calculus (3 of 5: Observing patterns in first principles)
  9. 9 Basics of Calculus (4 of 5: Considering the gradient function visually)
  10. 10 Basics of Calculus (5 of 5: Locating a tangent)
  11. 11 Calculus Notation & Terminology
  12. 12 First Principles Example: Square Root of x
  13. 13 First Principles Example: x²
  14. 14 First Principles Example: x³
  15. 15 First Principles for the Gradient Function
  16. 16 Prologue to Calculus
  17. 17 Calculus - Important Results (1 of 2)
  18. 18 Calculus - Important Results (2 of 2)
  19. 19 Chain Rule
  20. 20 Proving Product Rule
  21. 21 Quotient Rule
  22. 22 Why We Need The Product Rule
  23. 23 Product Rule - example question
  24. 24 Review - Basic Differentiation Rules
  25. 25 Continuity
  26. 26 Overview of Differentiation Rules
  27. 27 Differentiating the fourth root of x (by first principles)
  28. 28 Linear Rate of Change: Inlet+Outlet Valve Question
  29. 29 Linear Rate of Change: 2 Inlet Valves Question
  30. 30 What are Limits? (1 of 3: Approaching from Different Sides)
  31. 31 What are Limits? (2 of 3: A More Rigorous Definition)
  32. 32 What are Limits? (3 of 3: One Strategy for Evaluating Limits)
  33. 33 What is Continuity? (1 of 2: Definitions)
  34. 34 What is Continuity? (2 of 2: An Interesting Counter-Example)
  35. 35 Introduction to Calculus (1 of 2: Seeing the big picture)
  36. 36 Introduction to Calculus (2 of 2: First Principles)
  37. 37 Applying First Principles to x² (1 of 2: Finding the Derivative)
  38. 38 Applying First Principles to x² (2 of 2: What do we discover?)
  39. 39 Applying First Principles to x³
  40. 40 Finding the Equation of a Tangent
  41. 41 Deriving a Rule for Differentiating Powers of x
  42. 42 Differentiating Powers of x (1 of 4: Reviewing the Fundamentals)
  43. 43 Differentiating Powers of x (2 of 4: Considering the Hyperbola)
  44. 44 Differentiating Powers of x (3 of 4: First Principles & the Hyperbola)
  45. 45 Derivatives of Odd & Even Functions
  46. 46 Differentiating Powers of x (4 of 4: Square Root of x)
  47. 47 The Derivative of a Sum
  48. 48 Function of a Function Rule (1 of 4: Expanding Before Differentiating)
  49. 49 Function of a Function Rule (2 of 4: Introducing a Substitution)
  50. 50 Function of a Function Rule (3 of 4: Simple Example)
  51. 51 Function of a Function Rule (4 of 4: Working with Square Roots)
  52. 52 Product Rule (1 of 2: It's Complicated...)
  53. 53 Product Rule (2 of 2: Simple Example)
  54. 54 Where does the Product Rule come from? (1 of 2: Delta Notation)
  55. 55 Where does the Product Rule come from? (2 of 2: Derivation)
  56. 56 Quotient Rule (1 of 2: Derivation)
  57. 57 Quotient Rule (2 of 2: Simple Example)
  58. 58 Differentiability (1 of 3: Cube root of x)
  59. 59 Differentiability (2 of 3: Absolute Value of x)
  60. 60 Differentiability (3 of 3: x to the power of 2/3)
  61. 61 Differentiability (Formal Definition)
  62. 62 Properties of a Piecemeal Function (1 of 2: Testing Continuity)
  63. 63 Properties of a Piecemeal Function (1 of 2: Testing Differentiability)
  64. 64 Fundamental Definitions of Speed & Velocity
  65. 65 Instantaneous Velocity/Acceleration (1 of 2: Defining the Concepts)
  66. 66 Instantaneous Velocity/Acceleration (2 of 2: Example question)
  67. 67 Limits & Continuity (1 of 3: Formal intro to limits)
  68. 68 Limits & Continuity (2 of 3: Limits that exists when functions don't)
  69. 69 Limits & Continuity (3 of 3: Applications to graphs)
  70. 70 Continuity: Definitions & basic concept
  71. 71 The Problem of Tangents (1 of 4: Gradient as a function)
  72. 72 The Problem of Tangents (2 of 4: First Principles)
  73. 73 The Problem of Tangents (3 of 4: Gradient function of x²)
  74. 74 Applications of First Principles (1 of 4: Refining language and notation)
  75. 75 The Problem of Tangents (4 of 4: Finding a tangent's equation)
  76. 76 Applications of First Principles (2 of 4: The function 1/x)
  77. 77 Applications of First Principles (3 of 4: The function √x)
  78. 78 Applications of First Principles (4 of 4: Developing the power rule)
  79. 79 Product Rule (1 of 2: Derivation)
  80. 80 Review of Differentiation Rules
  81. 81 Product Rule (2 of 2: Applying it to example functions)
  82. 82 Quotient Rule (1 of 2: Derivation)
  83. 83 Quotient Rule (2 of 2: Examples & warnings)
  84. 84 Differentiating a Rational Function by First Principles
  85. 85 Finding the equation of a normal at a given point
  86. 86 Differentiating with Product & Chain Rule (example question)
  87. 87 The Differential Operator (1 of 2: Introduction to notation)
  88. 88 The Differential Operator (2 of 2: Example question)
  89. 89 Angle of Inclination (with Calculus)
  90. 90 Power Rule for Differentiation (1 of 4: Conjecture)
  91. 91 Power Rule for Differentiation (2 of 4: Background knowledge)
  92. 92 Power Rule for Differentiation (3 of 4: Derivation of rule)
  93. 93 Power Rule for Differentiation (4 of 4: Hyperbola)
  94. 94 Basics of Calculus, continued (1 of 2: Sum of functions)
  95. 95 Basics of Calculus, continued (2 of 2: Multiples of functions, constant function)
  96. 96 Leibniz's Derivative Notation (1 of 3: Overview)
  97. 97 Leibniz's Derivative Notation (2 of 3: Finding equation of a tangent)
  98. 98 Leibniz's Derivative Notation (3 of 3: Introducing the chain rule)
  99. 99 Using the Chain (Function of a Function) Rule
  100. 100 Product Rule - Definition
  101. 101 Quotient Rule (1 of 2: Proof from product & chain rule)
  102. 102 Quotient Rule (2 of 2: Worked examples)
  103. 103 Motion Graphs (1 of 2: Cannon Man's Displacement)
  104. 104 Motion Graphs (2 of 2: Cannon Man's Speed)
  105. 105 Review of Basic Differentiation (1 of 2: Polynomials, Products, Quotients)
  106. 106 Review of Basic Differentiation (2 of 2: Considering derivatives visually)
  107. 107 Calculus of Exponential Functions (1 of 4: Considering derivatives visually)
  108. 108 Calculus of Exponential Functions (2 of 4: The importance of 2.718...)
  109. 109 Calculus of Exponential Functions (3 of 4: Basic differentiation examples)
  110. 110 Calculus of Exponential Functions (4 of 4: Differentiating with non-e bases)
  111. 111 Determining Derivatives from Graphs (1 of 3: Identifying major features)
  112. 112 Determining Derivatives from Graphs (2 of 3: Considering sign of the gradient)
  113. 113 Determining Derivatives from Graphs (3 of 3: Reversing the process)

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free
Someone learning on their laptop while sitting on the floor.