### Course curriculum

• 1
##### Welcome to the course!
• How To Use This Course
• 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
• 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
• 4
##### Type 3: Product and Quotient Rules
• Applying the Product Rule Formula
• Combining Product Rule with Power Rule
• How to use the Quotient Rule
• 5
##### Type 4: Trigonometric Derivatives
• The Six Important Trig Derivatives to Remember
• How to Apply Product Rule and Power Rule to Trig Derivatives
• 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
• 7
##### Type 6: Exponential and Logarithmic Derivatives
• Applying Derivatives Rules to Exponential Functions
• Differentiating Logarithmic Functions
• Saving Time Using Log Properties in Differentiation
• 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
• 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
• 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
• 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
• 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
• 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