Introduction to Differentiation

Prologue to Calculus (1 of 5: How fast did Usain Bolt run?).
Prologue to Calculus (2 of 5: How can we measure more accurately?).
Prologue to Calculus (3 of 5: The difference quotient).
Prologue to Calculus (4 of 5: Exploring a parabola).
Prologue to Calculus (5 of 5: Gradient of the tangent).
Basics of Calculus (1 of 5: Foundational language & notation).
Basics of Calculus (2 of 5: Example of using first principles).
Basics of Calculus (3 of 5: Observing patterns in first principles).
Basics of Calculus (4 of 5: Considering the gradient function visually).
Basics of Calculus (5 of 5: Locating a tangent).
Calculus Notation & Terminology.
First Principles Example: Square Root of x.
First Principles Example: x².
First Principles Example: x³.
First Principles for the Gradient Function.
Prologue to Calculus.
Calculus - Important Results (1 of 2).
Calculus - Important Results (2 of 2).
Chain Rule.
Proving Product Rule.
Quotient Rule.
Why We Need The Product Rule.
Product Rule - example question.
Review - Basic Differentiation Rules.
Continuity.
Overview of Differentiation Rules.
Differentiating the fourth root of x (by first principles).
Linear Rate of Change: Inlet+Outlet Valve Question.
Linear Rate of Change: 2 Inlet Valves Question.
What are Limits? (1 of 3: Approaching from Different Sides).
What are Limits? (2 of 3: A More Rigorous Definition).
What are Limits? (3 of 3: One Strategy for Evaluating Limits).
What is Continuity? (1 of 2: Definitions).
What is Continuity? (2 of 2: An Interesting Counter-Example).
Introduction to Calculus (1 of 2: Seeing the big picture).
Introduction to Calculus (2 of 2: First Principles).
Applying First Principles to x² (1 of 2: Finding the Derivative).
Applying First Principles to x² (2 of 2: What do we discover?).
Applying First Principles to x³.
Finding the Equation of a Tangent.
Deriving a Rule for Differentiating Powers of x.
Differentiating Powers of x (1 of 4: Reviewing the Fundamentals).
Differentiating Powers of x (2 of 4: Considering the Hyperbola).
Differentiating Powers of x (3 of 4: First Principles & the Hyperbola).
Derivatives of Odd & Even Functions.
Differentiating Powers of x (4 of 4: Square Root of x).
The Derivative of a Sum.
Function of a Function Rule (1 of 4: Expanding Before Differentiating).
Function of a Function Rule (2 of 4: Introducing a Substitution).
Function of a Function Rule (3 of 4: Simple Example).
Function of a Function Rule (4 of 4: Working with Square Roots).
Product Rule (1 of 2: It's Complicated...).
Product Rule (2 of 2: Simple Example).
Where does the Product Rule come from? (1 of 2: Delta Notation).
Where does the Product Rule come from? (2 of 2: Derivation).
Quotient Rule (1 of 2: Derivation).
Quotient Rule (2 of 2: Simple Example).
Differentiability (1 of 3: Cube root of x).
Differentiability (2 of 3: Absolute Value of x).
Differentiability (3 of 3: x to the power of 2/3).
Differentiability (Formal Definition).
Properties of a Piecemeal Function (1 of 2: Testing Continuity).
Properties of a Piecemeal Function (1 of 2: Testing Differentiability).
Fundamental Definitions of Speed & Velocity.
Instantaneous Velocity/Acceleration (1 of 2: Defining the Concepts).
Instantaneous Velocity/Acceleration (2 of 2: Example question).
Limits & Continuity (1 of 3: Formal intro to limits).
Limits & Continuity (2 of 3: Limits that exists when functions don't).
Limits & Continuity (3 of 3: Applications to graphs).
Continuity: Definitions & basic concept.
The Problem of Tangents (1 of 4: Gradient as a function).
The Problem of Tangents (2 of 4: First Principles).
The Problem of Tangents (3 of 4: Gradient function of x²).
Applications of First Principles (1 of 4: Refining language and notation).
The Problem of Tangents (4 of 4: Finding a tangent's equation).
Applications of First Principles (2 of 4: The function 1/x).
Applications of First Principles (3 of 4: The function √x).
Applications of First Principles (4 of 4: Developing the power rule).
Product Rule (1 of 2: Derivation).
Review of Differentiation Rules.
Product Rule (2 of 2: Applying it to example functions).
Quotient Rule (1 of 2: Derivation).
Quotient Rule (2 of 2: Examples & warnings).
Differentiating a Rational Function by First Principles.
Finding the equation of a normal at a given point.
Differentiating with Product & Chain Rule (example question).
The Differential Operator (1 of 2: Introduction to notation).
The Differential Operator (2 of 2: Example question).
Angle of Inclination (with Calculus).
Power Rule for Differentiation (1 of 4: Conjecture).
Power Rule for Differentiation (2 of 4: Background knowledge).
Power Rule for Differentiation (3 of 4: Derivation of rule).
Power Rule for Differentiation (4 of 4: Hyperbola).
Basics of Calculus, continued (1 of 2: Sum of functions).
Basics of Calculus, continued (2 of 2: Multiples of functions, constant function).
Leibniz's Derivative Notation (1 of 3: Overview).
Leibniz's Derivative Notation (2 of 3: Finding equation of a tangent).
Leibniz's Derivative Notation (3 of 3: Introducing the chain rule).
Using the Chain (Function of a Function) Rule.
Product Rule - Definition.
Quotient Rule (1 of 2: Proof from product & chain rule).
Quotient Rule (2 of 2: Worked examples).
Motion Graphs (1 of 2: Cannon Man's Displacement).
Motion Graphs (2 of 2: Cannon Man's Speed).
Review of Basic Differentiation (1 of 2: Polynomials, Products, Quotients).
Review of Basic Differentiation (2 of 2: Considering derivatives visually).
Calculus of Exponential Functions (1 of 4: Considering derivatives visually).
Calculus of Exponential Functions (2 of 4: The importance of 2.718...).
Calculus of Exponential Functions (3 of 4: Basic differentiation examples).
Calculus of Exponential Functions (4 of 4: Differentiating with non-e bases).
Determining Derivatives from Graphs (1 of 3: Identifying major features).
Determining Derivatives from Graphs (2 of 3: Considering sign of the gradient).
Determining Derivatives from Graphs (3 of 3: Reversing the process).