Explore a comprehensive tutorial on derivatives, covering the definition, basic examples, and various rules including product, quotient, and chain rules. Delve into complex topics such as implicit differentiation, logarithmic differentiation, and derivatives of exponential, parametric, and trigonometric functions. Learn to sketch derivatives, solve instantaneous velocity problems, and apply the power rule. Master techniques for handling complicated derivative examples, including those involving factoring and simplification. Discover the applications of derivatives in position, velocity, and acceleration calculations, as well as in inverse trigonometric and hyperbolic functions.
Overview
Syllabus
Understanding the Definition of the Derivative.
Sketching the Derivative of a Function.
Finding a Derivative Using the Definition of a Derivative.
Derivative Using the Definition, Example 2.
Instantaneous Velocity Using Limit Definition of Derivative.
Instantaneous Velocity, Definition of Derivative.
Limit Definition of Derivative, Rational Function Example.
Derivative Using Definition: Rational Function Example.
Limit Definition of Derivative, Square Root Example.
Derivative of Root Function Using Definition of a Derivative.
Basic Derivative Rules - The Shortcut Using the Power Rule.
Power Rule and Derivatives, A Basic Example #1.
Power Rule and Derivatives, A Basic Example, #2.
Power Rule for Finding Derivatives, Basic Example #3.
Basic Derivative Examples.
More Derivative Examples, #1.
More Derivative Examples, #2.
More Derivative Examples, #3.
The Product Rule for Derivatives.
Derivatives using the Product Rule.
Proof of the Product Rule from Calculus.
The Quotient Rule.
Derivatives Using the Quotient Rule.
General Chain Rule , Partial Derivatives - Part 1.
General Chain Rule - Part 2.
Finding Derivatives using the Chain Rule.
Chain Rule for Finding Derivatives.
Basic Chain Rule Problems.
More Chain Rule Examples #1.
More Chain Rule Examples #2.
More Chain Rule Examples #3.
Using the Chain Rule - Harder Example #1.
Using the Chain Rule - Harder Example #2.
Using the Chain Rule - Harder Example #3.
Derivatives - Product + Chain Rule + Factoring.
Product Rule, Chain Rule and Factoring - Ex 2.
Derivatives - Quotient and Chain Rule and Simplifying.
More Complicated Derivative Examples.
More Complicated Derivative Examples.
❖ Lots of Different Derivative Examples! ❖.
Implicit Differentiation - Basic Idea and Examples.
Implicit Differentiation - Basic Example 1 / 3.
Implicit Differentiation - Basic Example 2 / 3.
Implicit Differentiation - Basic Example 3 / 3.
Using Implicit Differentiation - Extra Examples.
Using Implicit Differentiation - Example.
Using Implicit Differentiation to find a derivative.
Using Implicit Differentiation to find a Second Derivative.
Implicit Differentiation - More Examples.
More! Implicit Differentiation Examples.
More Implicit Differentiation Examples - 3.
❖ Derivatives of Logarithmic Functions ❖.
Derivatives of Logarithm Functions - 1 of 2.
Derivatives of Logarithm Functions - 2 of 2.
Derivatives of Logarithmic Functions and Examples.
Derivatives of Logarithmic Functions - More Examples.
Logarithmic Differentiation.
Logarithmic Differentiation - Example 2.
Logarithmic Differentiation - Example 3.
Derivatives of Exponential Functions.
Derivatives of Exponential Functions.
Derivatives of Exponential Functions and Examples.
Exponential Functions and Derivatives, More Example #1.
Derivatives of Parametric Functions.
Derivatives of Parametric Equations, Another Example #1.
Derivatives of Parametric Equations, Another Example #2 - Second Derivative.
Parametric Curves - Finding Second Derivatives.
More Derivatives Involving Trigonometric Functions, Ex 1.
More Derivatives Involving Trigonometric Functions, Ex 2.
Deriving the Derivative Formulas for Tangent, Cotangent, Secant, Cosecant.
Inverse Trigonometric Functions - Derivatives.
Derivatives of Inverse Trigonometric Functions - Another Example!.
Deriving the Derivative of Inverse Tangent or y = arctan (x).
Derivative of a Vector Function - Another Ex 1.
Inverse Trigonometric Functions - Derivatives - Example 2.
Inverse Trigonometric Functions - Derivatives - Example 3.
Hyperbolic Functions - Derivatives.
Inverse Hyperbolic Functions - Derivatives.
Position, Velocity, Acceleration using Derivatives.
Taught by
patrickJMT
