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Unit 2: Differentiation-Limit Definition and Fundamental Properties

What is a Derivative?

What is a Derivative?

Algebra vs. Calculus

Average Rate of Change and Slope of Tangent Line Examples from Actual AP Exams

Is it Differentiable?

Differentiability Examples From Actual AP Exams

Derivative Notation and Language

Limit Definition of the Derivative (The Long Way)

Limit Definition of the Derivative Examples from Actual AP Exams

Meaning: Limit Definition of the Derivative

Identifier: Limit Definition of the Derivative

Method: Limit Definition of the Derivative

Example 1: Limit Definition of the Derivative

Example 1: Limit Definition of the Derivative (Video)

The 5 Main Derivative Rules

5 Main Derivative Rules

Always Step 1: Simplify and Look for Algebraic Rewrites.

Roots or Radicals

x’s on the Bottom of a Fraction

Trig Functions Raised to a Power

Look to Make Your Life Easier

Rule 1: Constants

Identifier: Derivative of Constants

Method: Derivative of Constants

Example 1: Derivative of a Constant

Rule 2: Power Rule

Power Rule Examples from Actual AP Exams

Identifier: Power Rule Derivative

Method: Power Rule Derivative

Example 1: Power Rule Derivative

Example 1: Power Rule Derivative (Video)

Example 2: Power Rule Derivative

Example 2: Power Rule Derivative (Video)

Example 3: Power Rule Derivative

Example 3: Power Rule Derivative (Video)

Rule 3: Product Rule

Product Rule Examples from Actual AP Exams

Identifier: Product Rule Derivative

Method: Product Rule Derivative

Example 1: Product Rule Derivative

Example 1: Product Rule Derivative (Video)

Rule 4: Quotient Rule

Quotient Rule Derivative Examples from Actual AP Exams

Identifier: Quotient Rule Derivative

Method: Quotient Rule Derivative

Example 1: Quotient Rule Derivative

Example 1: Quotient Rule Derivative (Video)

Rule 5: Chain Rule

Chain Rule Examples From Actual AP Exams

Identifier: Chain Rule Derivative

Method: Chain Rule Derivative

Example 1: Chain Rule Derivative

Example 1: Chain Rule Derivative (Video)

Special Case Derivatives: Your new multiplication tables

Special Case Derivatives Overview

Six Trig Functions

Trig Function Derivative Examples From Actual AP Exams

Identifier: Trig Function Derivatives

Method: Trig Function Derivatives

Example 1: Trig Function Derivatives

Example 1: Trig Function Derivatives (Video)

Example 2: Trig Function Derivatives

Example 2: Trig Function Derivatives (Video)

Six Inverse Trig Functions

Inverse Trig Derivative Examples from Actual AP Exams

Identifier: Inverse Trig Derivatives

Method: Inverse Trig Derivatives

Example 1: Inverse Trig Derivatives

Example 1: Inverse Trig Derivatives (Video)

Example 2: Inverse Trig Derivatives

Example 2: Inverse Trig Derivatives (Video)

e^{x}

Derivative of ‘e’ Examples From Actual AP Exams

Identifier: e^(x) Derivative

Method: e^(x) Derivatives

Example 1: e^(x) Derivative

Example 1: e^(x) Derivative (Video)

\ln (x)

Derivative of ln(x) Examples From Actual AP Exams

Identifier: ln(x) Derivative

Method: ln(x) Derivative

Example: ln(x) Derivative

Example: ln(x) Derivative (Video)

a^{x}

= Any number raised to the x

Identifier: a^(x) Derivative

Method: a^(x) Derivative

Example 1: a^(x) Derivative

Example 1: a^(x) Derivative (Video)

\log_{b} (x)

Identifier: Logarithm Derivative

Method: Logarithm Derivative

Example 1: Logarithm Derivative

Example 1: Logarithm Derivative (Video)

f^{- 1} ((x))

= Inverse Function

Derivative of Inverse Functions Examples from Actual AP Exams

Identifier: Inverse Function Derivative

Method: Inverse Function Derivative

Example 1: Inverse Function Derivative

Example 1: Inverse Function Derivative (Video)

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Previous Lesson

Identifier: a^(x) Derivative

Unit 2: Differentiation-Limit Definition and Fundamental Properties
a x = Any number raised to the x
Identifier: a^(x) Derivative

Some part of your equation contains the base case $a^{(x)}$ , any number raised to the x .

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