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Introduction to Calculus 1: Differentiation

Name: Introduction to Calculus 1: Differentiation
Rating: 4.5 (38 reviews)

Learn the basic methods of differential calculus

Created byGina Chou

Last updated 1/2025

English

What you'll learn

Find limits of functions (graphically, numerically and algebraically)
Analyze and apply the notions of continuity and differentiability to algebraic and transcendental functions
Determine derivatives by a variety of techniques including explicit differentiation, implicit differentiation, and logarithmic differentiation
Find higher order derivatives

Course content

5 sections • 41 lectures • 4h 56m total length

Overview3:15
Welcome and How It Works1:33
Tips to Maximize Your Learning0:34

What's in this Review Section0:29
Algebra8:23
Review algebra basics by factoring polynomials, extracting the greatest common factor, and applying differences of squares and cubes, then factor quadratics to rewrite them in factored form.
Functions: Graphing12:43
Function: Domain and Range5:24
Functions: Asymptotes1:26
Identify horizontal and vertical asymptotes in functions like 1/x and e^x, noting x=0 yields a vertical asymptote and y=0 a horizontal asymptote. Preview methods to find them, including composition functions.
Functions: Composition Functions2:48
Functions: Inverse Functions6:58
Limits and Continuity8:30
Explore limits and continuity, including left and right limits, vertical and horizontal asymptotes, and pivotal algebraic techniques. Define continuity and distinguish removable versus jump discontinuities using one-sided limits.
Review Topics
Limits
Continuity

Downloadable Notes0:03
Secant and Tangent Lines11:09
Definition of Derivative Function13:39
Explore the derivative function as the slope of tangents, defined by a limit, with examples like f(x)=x^2 and g(x)=square root of x, and learn to derive and tangent-line equations.
Power Rule11:59
Develop and apply the power rule to find derivatives of x^n, including constants, and recognize patterns from examples like x^3, sqrt(x), and 1/x^8, with constants' derivatives equal to zero.
Derivative Notation3:48
Constant Multiple Rule5:17
Learn the constant multiple rule, pulling constants outside derivatives, and apply the power rule to negative and fractional exponents, with a quick limit-based justification.
Sum and Difference Rules4:38
Product Rule10:37
Quotient Rule13:37
Differentiability13:44
Normal Line4:27
The normal line is perpendicular to the tangent line. With f(x)=4x^4+x+1 at x=1, the tangent slope is 17, so the normal line is y=-1/17 x+103/17.
Derivatives and Differentiability
Higher Derivatives4:10
Chain Rule12:18
Implicit Differentiation13:09
Learn how implicit differentiation derives dy/dx for equations implicitly defining y, such as x^2 + y^2 = 25 and y^2 = 2x, by differentiating both sides and solving for y'.
Example: Implicit Differentiation3:26
Higher Derivative, Chain Rule, Implicit Differentiation

Downloadable Notes0:03
Review on Trigonometric Functions8:31
Derivatives of Trigonometric Functions19:39
Examples: Derivatives of Trigonometric Functions4:49
Inverse Trigonometric Functions6:30
Derivatives of Inverse Trigonometric Functions11:11
Review on Exponential and Log Rules11:14
Derivatives of Exponential and Log Function11:28
Log Differentiation9:57
Examples: Log Differentiation8:00
Derivatives of Transcendental Functions

Requirements

Precalculus (algebra, trigonometry, and functions)
Familiarity with limits and continuity

Description

HOW THIS COURSE WORK:

This course, Introduction to Calculus 1: Differentiation, has everything you need to know about derivatives in Calculus 1, including video, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and theorems. The course is organized into the following sections:

Introduction
Review: Precalculus, Limits, and Continuity
Differentiation (derivative rules and techniques)
Derivatives of Transcendental Functions (trig., exp., log.)
Conclusion

CONTENT YOU WILL GET INSIDE EACH SECTION:

Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.

Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).

Extra notes: I provide some extra notes, including formula sheets and some other useful study guidance.

Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.

THINGS THAT ARE INCLUDED IN THE COURSE:

An instructor who truly cares about your success
Lifetime access to Introduction to Calculus 1: Differentiation
Friendly support in the Q&A section
Udemy Certificate of Completion available for download

BONUS #1: Downloadable lectures so you can watch whenever and wherever you are.

BONUS #2: Downloadable lecture notes and some extra notes (i.e. formula sheet) so you can review the lectures without having a device to watch/listen.

BONUS #3: The review section on precalculus, limits, and continuity.

BONUS #4: Nine assignments with solutions for Calculus 1 in total that make you productive while taking the course. (assignments 1-6 are available for this introductory course)

BONUS #5: Step-by-step guide to help you solve problems.

BONUS #6: Two bonus lectures on the applications of derivatives.

See you inside the course!

- Gina :)

Who this course is for:

Anyone who has completed precalculus (algebra and trigonometry) and wants to learn some more advanced math (i.e. calculus)
Current calculus students who are looking for extra help on differentiation
Anyone who is not in science stream but wants to study calculus for fun

Introduction to Calculus 1: Differentiation

What you'll learn

Explore related topics

Course content

Introduction3 lectures • 5min

Review8 lectures • 47min

Differentiation15 lectures • 2hr 6min

Derivatives of Transcendental Functions10 lectures • 1hr 31min

Conclusion5 lectures • 27min

Requirements

Description

Who this course is for: