This course on derivatives aims to help learners understand the fundamental concepts and applications of derivatives in calculus. By the end of the course, students will be able to calculate derivatives using various rules such as the power rule, product rule, quotient rule, and chain rule. The course covers topics like the derivative of trigonometric functions, implicit differentiation, and inverse functions. The teaching method involves theoretical explanations followed by examples and proofs to reinforce learning. This course is intended for students studying calculus or anyone interested in deepening their understanding of derivatives in mathematics.
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
