The 17 Essential Topics to Master Differentiation

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How To Use This Course

Download the Differentiation Cheat Sheet Here

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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

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Power Rule Formula

Rules for Addition and Subtraction of Derivatives

Power Rule Applied to Negatives, Decimals and Fractions

Solved Examples

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Applying the Product Rule Formula

Combining Product Rule with Power Rule

How to use the Quotient Rule

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The Six Important Trig Derivatives to Remember

How to Apply Product Rule and Power Rule to Trig Derivatives

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The Three Steps for the Chain Rule

Solved Examples using the Three Steps

Using the the Single Line Technique to Speed Up

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Applying Derivatives Rules to Exponential Functions

Differentiating Logarithmic Functions

Saving Time Using Log Properties in Differentiation

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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

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Implicit Equations and Their Differentiation

Finding y' using Implicit Differentiation

How to Use Implicit Differentiation to find the Tangent Line to a Curve

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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

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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

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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

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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

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The 3 Steps to Solve Optimization Problems

An Important Solved Example: Optimizing Rectangles

Solved Example: Optimizing a Cylindrical Can

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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

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The 3Step Method to Solve Related Rates Problems

Solved Example

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The 3 Step Method to Solve Linear Approximation Problems

Solved Example

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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

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Congrats! Here's what's next...

Practice Workbook