What you'll learn

How to differentiate any kind of function
Special derivatives
Fundamental operations
Differentiation techniques
How to differentiate based on the definition of derivatives
How to differentiate implicit functions
How to differentiate parametric functions
How to determine the equation of tangent lines

Course content

8 sections • 45 lectures • 2h 23m total length

Introduction2:20

Derivative3:51
Definition of derivatives. Graphical meaning of derivatives.
Differentiation based on definition - 1. Example4:57
Example of calculating the derivative based on its definition.
Differentiation based on definition - 2. Example2:56
Example of calculating the derivative based on its definition.
Differentiability3:09
Necessary and sufficient condition of differentiability.
Differentiability - 1. Example5:48
Example of checking the differentiability of a function at a given point.
Differentiability - 2. Example3:46
Example of checking the differentiability of a function at a given point.
Checkpoint - Differentiation based on definition0:06
Sample problems for you!

Special derivatives6:28
Derivatives of common functions.
Fundamental operations3:03
Fundamental operational rules. Sum rule, difference rule, product rule, quotient rule, chain rule.
Differentiation - 1. Example1:53
Example of differentiating polynomials.
Differentiation - 2. Example2:53
Example of using the product rule.
Differentiation - 3. Example2:17
Example of using the quotient rule.
Differentiation - 4. Example3:56
Example of using the chain rule.
Differentiation - 5. Example5:00
Differentiation - 6. Example3:36
Harder sample problem.
Differentiation - 7. Example3:31
Harder sample problem.
Differentiation - 8. Example3:10
Harder sample problem.
Checkpoint - Differentiation based on special derivatives0:06
Sample problems for you!

Differentiation of parametric functions4:42
Parametric function definition. Differentiation of parametric functions.
Differentiation of parametric functions - 1. Example3:09
Example of differentiating parametric functions.
Differentiation of parametric functions - 2. Example2:02
Example of differentiating parametric functions.
Polar coordinates3:57
Definition of polar coordinates. Connection between Cartesian and polar coordinates.
Differentiation in case of polar coordinates - 1. Example2:39
Example of differentiating parametric functions given by polar coordinates.
Differentiation in case of polar coordinates - 2. Example2:43
Example of differentiating parametric functions given by polar coordinates.
Checkpoint - Differentiation of parametric functions0:06
Sample problems for you!

Tangent lines4:16
Equation of the tangent line.
Tangent lines in case of explicit functions - 1. Example3:41
Example of determining the tangent line at a given point in case of explicitly given functions.
Tangent lines in case of explicit functions - 2. Example3:04
Example of determining the tangent line at a given point in case of explicitly given functions.
Tangent lines in case of implicit functions - 1. Example4:59
Example of determining the tangent line at a given point in case of implicitly given functions.
Tangent lines in case of implicit functions - 2. Example3:13
Example of determining the tangent line at a given point in case of implicitly given functions.
Tangent lines in case of parametric functions - 1. Example4:18
Example of determining the tangent line at a given point in case of parametricly given functions.
Tangent lines in case of parametric functions - 2. Example2:34
Example of determining the tangent line at a given point in case of parametricly given functions.
Tangent lines in case of polar coordinates - 1. Example4:54
Example of determining the tangent line at a given point in case of functions given by a polar equation.
Tangent lines in case of polar coordinates - 2. Example3:02
Example of determining the tangent line at a given point in case of functions given by a polar equation.
Checkpoint - Tangent lines0:06
Sample problems for you!

Requirements

An average highschool level mathematics knowledge
A desire to get better in mathematics
A knowledge of the limits of functions is advantageous but not necessary for most of the course

Description

Welcome!

By completing this course, you are going to be able to determine the derivative of any kind of function. I'm going to show you the necessary theoretical background in a nutshell. Then I show you lots of practical examples! I believe that you should always learn through solving problems! That's why I made this course practical and I also give you a chance to practice on your own!

The course starts from the definition of the derivatives and goes through the differentiation techniques one by one. In every section, the theory is summarized briefly and then I show more and more complicated numerical examples. These sample problems are going to help you understand what you have to do! Finally, there is always a checkpoint at the end of a section to test your knowledge!

I believe in learning through examples so the course is highly practical. If you want to practice even more, you can stop the videos and make an effort of solving the numerical examples by yourself! Or at least you can solve the problems I give you at the checkpoints!

You don't need much of a prior knowledge to take this course. If you know the basic operations and some details about the basic functions, you are good to go! To understand the differentiation based on the definition of the derivatives, you need some background in calculating the limits of functions. If you only need to learn how to differentiate functions as a whole, you do not even need to know about limits. I'm going to clear the necessary details during the lectures, so do not worry about the challenge!

This course is primarily designed for university/college students who are learning single-variable Calculus and have to deal with derivatives. If you are struggling with this topic, let me help you! Here you are going to get every help that you possibly need! If you have already completed this topic but you feel like you need to practice the basics, you are also welcome in this course!

I hope I can help you with this course just like I've already helped more than 6000 students with my other courses! I can't wait to see you inside! Have fun and learn a lot!

Note: this course covers the topic of single-variable derivatives. This is introductory level calculus. If you hear about derivatives for the first time, this is your course! If you need multi-variable differentiation (partial derivatives), you should look for an other course. Check out the curriculum for details!

Who this course is for:

Anyone who is about to take a test/exam in the topic of Differentiation
Anyone who is currently learning Calculus
Anyone who is interested in the differentitation methods

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 2min

Differentiation based on definition7 lectures • 25min

Differentiation based on special derivatives11 lectures • 36min

Implicit differentiation4 lectures • 16min

Differentiation of parametric functions7 lectures • 19min

Tangent lines10 lectures • 34min

Taylor polynomial4 lectures • 11min

Thank you!1 lecture • 1min

Requirements

Description

Who this course is for: