Explore the fundamentals of calculus in this comprehensive video series on derivatives. Begin with an introduction to the concept, learn the definition, and work through various examples to solidify understanding. Dive into basic rules, including the power rule, exponential function, and constant and sum rules, with proofs and practical applications. Progress to more advanced topics such as product and quotient rules, chain rule, implicit differentiation, and inverse functions. Master the differentiation of trigonometric functions and their inverses, and gain insight into higher-order derivatives. Through numerous examples and step-by-step explanations, develop a strong foundation in calculus and enhance problem-solving skills in this essential mathematical subject.
Overview
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.
Taught by
Sean Fitzpatrick
