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# APEX Calculus: Chapter 2 - Derivatives

### Syllabus

Derivatives: Intro - 01. Introduction.
Derivatives: Intro - 02. Definition.
Derivatives: Intro - 03. Example (first version).
Derivatives: Intro - 04. Example (second version).
Derivatives: Intro - 05. Derivative As a Function.
Derivatives: Intro - 06. Notation.
Derivatives: Intro - 07. Example.
Derivatives: Intro - 08. Derivative of sin(x).
Derivatives: Intro - 09. Derivative of cos(x).
Derivatives: Intro - 10. Differentiable Implies Continuous.
Derivatives: Intro - 11. Example.
Derivatives: Basic Rules - 01. Simplest.
Derivatives: Basic Rules - 02. Power Rule.
Derivatives: Basic Rules - 03. Example.
Derivatives: Basic Rules - 04. Exponential function.
Derivatives: Basic Rules - 05. Constant and Sum Rules.
Derivatives: Basic Rules - 06. Proofs.
Derivatives: Basic Rules - 07. Examples.
Derivatives: Basic Rules - 08. Higher Order Derivatives.
Derivatives: Basic Rules - 09. Examples.
Derivatives: Product and Quotient - 01. Product Intro.
Derivatives: Product and Quotient - 02. Product Example.
Derivatives: Product and Quotient - 03. Proof of Product rule.
Derivatives: Product and Quotient - 04. Example.
Derivatives: Product and Quotient - 05. Example With 3 Functions.
Derivatives: Product and Quotient - 06. Example With 4 Functions.
Derivatives: Product and Quotient - 07. Quotient Rule.
Derivatives: Product and Quotient - 08. Example.
Derivatives: Product and Quotient - 09. tan(x).
Derivatives: Product and Quotient - 10. Negative Powers.
Derivatives: Product and Quotient - 11. Example - simplify first.
Derivatives: Chain - 01. Intro.
Derivatives: Chain - 02. Theorem.
Derivatives: Chain - 03. Examples.
Derivatives: Chain - 04. Examples.
Derivatives: Chain - 05. Example With 3 Functions.
Derivatives: Chain - 06. General Power and Exponential.
Derivatives: Implicit - 01. Intro.
Derivatives: Implicit - 02. Circle.
Derivatives: Implicit - 03. Example.
Derivatives: Implicit - 04. Tangent Line For Previous Example.
Derivatives: Implicit - 05. Example.
Derivatives: Implicit - 06. Example.
Derivatives: Implicit - 07. Second Derivative.
Derivatives: Implicit - 08. Example.
Derivatives: Implicit - 09. Logarithmic.
Derivatives: Implicit - 10. Using inverse relationship of ln and exp.
Derivatives: Implicit - 11. Example.
Derivatives: Inverse - 01. Intro.
Derivatives: Inverse - 02. Properties.
Derivatives: Inverse - 03. Examples.
Derivatives: Inverse - 04. Inverse Function Theorem.
Derivatives: Inverse - 05. Restricting Domain.
Derivatives: Inverse - 06. Derivative of arcsin.
Derivatives: Inverse - 07. Derivative of arctan.

Sean Fitzpatrick

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