\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \( \newcommand{\arcsinh}{ \, \mathrm{arcsinh} \, } \) \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) \( \newcommand{\arcsech}{ \, \mathrm{arcsech} \, } \) \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \)

17Calculus Derivatives - Differentials

Limits

Using Limits

Limits FAQs

Derivatives

Graphing

Applications

Derivatives FAQs

Integrals

Improper Integrals

Trig Integrals

Length-Area-Volume

Applications - Tools

Infinite Series

Applications

Tools

Parametrics

Conics

Polar Coordinates

Practice

Practice Problems

Practice Exams

Tools

Calculus Tools

Additional Tools

Articles

Derivatives

Graphing

Applications

Derivatives FAQs

SV Calculus

MV Calculus

Practice

Practice Problems

Practice Exams

Tools

Calculus Tools

Additional Tools

Articles

The basic idea of differentials is based in notation. By now you know that, given a function \(y=f(x)\), we write the derivative with respect to x as \(\displaystyle{ \frac{dy}{dx} = f'(x) }\). Remember that the notation \(\displaystyle{ \frac{dy}{dx} }\) does NOT mean dy divided by dx. The notation is actually shorthand for \(\displaystyle{ \frac{d}{dx}[y] }\).

HOWEVER, that said, we can actually write this a bit differently as \(\displaystyle{ \frac{dy}{dx} = f'(x) \to dy = f'(x)~dx }\). This notation gives the impression that we are dividing dy by dx but it takes a lot of math to make this transition. So please don't take this for granted.

This new form of the derivative is called the differential form. For examples see Paul's Online Notes Differentials page.

Note - There are other details about differentials that we do not yet cover here. Paul's Online Notes Differentials page has some explanation and examples. Also, here is a playlist with some videos that may help you.

You CAN Ace Calculus

Topics You Need To Understand For This Page

Related Topics and Links

To bookmark this page, log in to your account or set up a free account.

Topics Listed Alphabetically

Single Variable Calculus

Multi-Variable Calculus

Differential Equations

Precalculus

Search Practice Problems

Do you have a practice problem number but do not know on which page it is found? If so, enter the number below and click 'page' to go to the page on which it is found or click 'practice' to be taken to the practice problem.

how to take good notes

Get great tutoring at an affordable price with Chegg. Subscribe today and get your 1st 30 minutes Free!

The 17Calculus and 17Precalculus iOS and Android apps are no longer available for download. If you are still using a previously downloaded app, your app will be available until the end of 2020, after which the information may no longer be available. However, do not despair. All the information (and more) is now available on 17calculus.com for free.

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

Save Up To 50% Off SwissGear Backpacks Plus Free Shipping Over $49 at eBags.com!

Try Amazon Music Unlimited Free Trial

How to Develop a Brilliant Memory Week by Week: 50 Proven Ways to Enhance Your Memory Skills

Save Up To 50% Off SwissGear Backpacks Plus Free Shipping Over $49 at eBags.com!

Shop Amazon - Rent eTextbooks - Save up to 80%

Do NOT follow this link or you will be banned from the site!

When using the material on this site, check with your instructor to see what they require. Their requirements come first, so make sure your notation and work follow their specifications.

DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site are used or how they affect the grades or projects of any individual or organization. We have worked, to the best of our ability, to ensure accurate and correct information on each page and solutions to practice problems and exams. However, we do not guarantee 100% accuracy. It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. How each person chooses to use the material on this site is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject. In short, use this site wisely by questioning and verifying everything. If you see something that is incorrect, contact us right away so that we can correct it.

Links and banners on this page are affiliate links. We carefully choose only the affiliates that we think will help you learn. Clicking on them and making purchases help you support 17Calculus at no extra charge to you. However, only you can decide what will actually help you learn. So think carefully about what you need and purchase only what you think will help you.

We use cookies on this site to enhance your learning experience.

17calculus

Copyright © 2010-2020 17Calculus, All Rights Reserved     [Privacy Policy]     [Support]     [About]

mathjax.org
Real Time Web Analytics
17Calculus
We use cookies to ensure that we give you the best experience on our website. By using this site, you agree to our Website Privacy Policy.