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Calculus 1 Derivatives of Math Functions Review Course

Differentiation of Polynomial, Rational, Radical, Exponential, Trigonometric and Logarithmic Functions.
Instructor:
Julio Gonzalez
267 students enrolled
English [Auto]
This course will help you to master your ability to find the derivative of a function.

This calculus 1 derivatives course focuses on differentiating functions.  It explains how to find the derivatives of functions that you will typically encounter in your first semester calculus.  This course is for university students taking college calculus and high school students who are taking AP Calculus AB.

Here is a list of topics:

1.  Derivatives of Constants

2.  The Power Rule and Constant Multiple Rule

3.  Derivatives of Rational Functions

4.  Derivatives of Square Root and Radical Functions

5.  How to Differentiate Polynomial Functions Using The Sum and Difference Rule

6.  Derivatives of Trigonometric Functions – sin, cos, tan, sec, cot, csc

7.  Average Rate of Change vs Instantaneous Rate of Change

8.  Writing Equations of the Tangent Line

9.  Limit Definition of the Derivative Process

10.  Alternative Form of Limit Definition of Derivative 

11.  Derivatives of Exponential Functions

12.  Derivatives of Natural Log Functions – Ln x

13.  Differentiation of Logarithmic Functions

14.  The Product rule and Quotient Rule

15.  The Chain Rule – Plenty of Examples

16.  Implicit Differentiation

17.  Derivatives of Inverse Trigonometric Functions

18.  Logarithmic Differentiation

19.  Free Response Video Quiz

Introduction

1
Introduction

This is an introductory video.

Derivatives Review

1
The Constant Rule

This video explains how to find the derivative of a constant which is always zero by the way.

2
The Power Rule

This tutorial explains how to differentiate a monomial using the power rule.

3
The Constant Multiple Rule

This video discusses the use of the constant multiple rule which is used to differentiate a monomial with a constant in front of it.  The power rule is required for this process as well.

4
Derivatives of Rational Functions

This video explains how to find the derivative of a rational function in the form of a fraction using the power rule.  You need to rewrite the function before you differentiate it.

5
Derivatives of Square Roots and Radical Functions

This lesson explains how to find the derivative of square root and radical functions by rewriting the function and using the power rule.

6
Derivatives of Basic Trigonometric Functions

This tutorial provides a basic introduction into the derivatives of the six trigonometric functions - sine, cosine, tangent, cotangent, cosecant, and secant.

7
Sum and Difference Rules

This video explains how to differentiate polynomial functions using the sum and difference rule.

8
Average Rate of Change vs Instantaneous Rate of Change

This tutorial explains how to calculate the average rate of change of a function and the instantaneous rate of change as well.  The instantaneous rate of change is equal to the slope of the tangent line which touches the graph at a single point.  The average rate of change is equivalent to the slope of the secant line which touches the graph at two points.

9
Estimating The Instantaneous Rate of Change Given a Table of Values

This video tutorial explains how to estimate the instantaneous rate of change given a table of values using the average rate of change formula.

10
Tangent Line Equation

This video explains how to write the equation of the tangent line given a function and an x value.

11
Limit Definition of The Derivative

This lecture explains how to find the derivative function using the limit process.

12
More Examples With Limits and Derivatives

This video provides more examples on limits and derivatives.

13
Alternative Form of the Limit Derivative Function

This tutorial explains how to calculate the instantaneous rate of change or slope of the tangent line using the alternative form of the limit derivative formula.

14
Derivatives of Exponential Functions

This lecture explains how to find the derivative of exponential functions.

15
Derivative of Natural Log Functions

This video lesson discusses how to differentiate natural log functions using a simple formula.

16
Derivatives of Logarithmic Functions

This tutorial explains how to find the derivative of logarithmic functions using a simple formula.

17
The Product Rule

This tutorial explains how to find the derivative of two functions multiplied to each other using the product rule.

18
The Quotient Rule

This tutorial explains how to find the derivative of a division of two functions using the quotient rule.

19
The Chain Rule

This lesson provides many examples of finding the derivative of a composite function using the chain rule.

20
Implicit Differentiation

This video explains how to find the derivative of an equation with x and y variables using implicit differentiation.

21
Inverse Trig Functions

This video explains how to find the derivative of an inverse trigonometric function such as sin^-1 or arctangent.

22
Logarithmic Differentiation

This tutorial explains how to differentiate a function with a variable raised to another variable using logarithmic differentiation.

23
Video Quiz 1

This free response video quiz contains 5 questions with the solutions.  It's recommended to pause the video first and work on the problem before viewing the solution.

24
Video Quiz 2

This video quiz also contains 5 free response questions which covers some of the differentiation techniques covered in this course module.

You can view and review the lecture materials indefinitely, like an on-demand channel.
Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don't have an internet connection, some instructors also let their students download course lectures. That's up to the instructor though, so make sure you get on their good side!
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Includes

2 hours on-demand video
Full lifetime access
Access on mobile and TV
Certificate of Completion