Course curriculum

  • 1
    Welcome to the course!
    • How To Use This Course
    • Download the Differentiation Cheat Sheet Here
  • 2
    Type 1: What is a Derivative?
    • 1. What Happens When Speed Changes
    • 2. How to Calculate A Difference Quotient
    • 3. The Relation Between Derivative and Difference Quotient
    • 4. Names and Notations in Derivatives
    • Test Your Learning
  • 3
    Type 2: Power Rule
    • Power Rule Formula
    • Rules for Addition and Subtraction of Derivatives
    • Power Rule Applied to Negatives, Decimals and Fractions
    • Solved Examples
    • Test Your Learning
  • 4
    Type 3: Product and Quotient Rules
    • Applying the Product Rule Formula
    • Combining Product Rule with Power Rule
    • How to use the Quotient Rule
    • Test Your Learning
  • 5
    Type 4: Trigonometric Derivatives
    • The Six Important Trig Derivatives to Remember
    • How to Apply Product Rule and Power Rule to Trig Derivatives
    • Test Your Learning
  • 6
    Type 5: Chain Rule
    • The Three Steps for the Chain Rule
    • Solved Examples using the Three Steps
    • Using the the Single Line Technique to Speed Up
    • Test Your Learning
  • 7
    Type 6: Exponential and Logarithmic Derivatives
    • Applying Derivatives Rules to Exponential Functions
    • Differentiating Logarithmic Functions
    • Saving Time Using Log Properties in Differentiation
    • Test Your Learning
  • 8
    Type 7: Tangents and Normals to a Curve
    • Deriving the Equation to a Tangent using Differentiation
    • Solved Example #1: Applying Derivatives To Find Tangents
    • Solved Example #2: Applying Derivatives To Find Tangents
    • The Two Important Types of Tangents: Horizontals and Verticals
    • Solved Examples of Horizontal and Vertical Tangents
    • Calculating the Normal Line to a Curve
    • Test Your Learning
  • 9
    Type 8: Implicit Differentiation
    • Implicit Equations and Their Differentiation
    • Finding y' using Implicit Differentiation
    • How to Use Implicit Differentiation to find the Tangent Line to a Curve
    • Test Your Learning
  • 10
    Type 9: "Optimization"
    • Understanding Critical Points
    • Interpreting Tangents Drawn at Critical Points
    • The Relationship between Maxima/Minima and Critical Points
    • Connecting Critical Points, Tangents and Max/Min Values
    • Test Your Learning
  • 11
    Type 10: The First Derivative Test
    • Understanding the Behavior of f'(x) around Critical Points
    • Solved Examples: How to Apply the First Derivative Test
    • Special Case: When f'(x) does not Change its Sign
    • Test Your Learning
  • 12
    Type 11: The Second Derivative Test
    • Using the f''(x) to Determine if Critical Points are Maxima or Minima
    • Solved Example: How to Apply the Second Derivative Test
    • Factoring: An Important Skill in Calculating Critical Points
    • What Happens When f''(x) = 0
    • Test Your Learning
  • 13
    Type 12: Curve Sketching
    • How to Sketch a Curve using Sign Analysis Charts
    • Concavity
    • Sketching f(x) when a Signal Analysis Chart is given
    • How to Sketch f(x) based on a Sketch of f'(x)
    • How
  • 14
    Type 13: Optimization - Word Problems
    • The 3 Steps to Solve Optimization Problems
    • An Important Solved Example: Optimizing Rectangles
    • Solved Example: Optimizing a Cylindrical Can
  • 15
    Type 14: The 3 Theorems of Differentiation
    • The 3 Conditions for Rolle's Theorem
    • Solved Examples for Rolle's Theorem
    • The 2 Conditions for the Mean Value Theorem, Solved Examples
    • Examples where the Mean Value Theorem Does Not Apply
  • 16
    Type 15: Related Rates
    • The 3-Step Method to Solve Related Rates Problems
    • Solved Example
  • 17
    Type 16: Linear Approximations
    • The 3 Step Method to Solve Linear Approximation Problems
    • Solved Example
  • 18
    Type 17: L'Hopital's Rule
    • L'Hopital's Rule for 0/0 and ∞/∞ Forms
    • L'Hopital's Rule for 0 * ∞ and ∞ - ∞ Forms
    • L'Hopital's Rule for 0^∞ and ∞^0 Forms
  • 19
    Next steps
    • Congrats! Here's what's next...
    • Practice Workbook