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Introduction to Differentiation

Introduction to Differentiation

Eddie Woo via YouTube Direct link

Differentiability (Formal Definition)

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Differentiability (Formal Definition)

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Introduction to Differentiation

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  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)

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