New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Differentials, Chainr Rule and Directional Derivatives

by: Saul Cervantes

Differentials, Chainr Rule and Directional Derivatives Math 2419

Marketplace > University of Texas at Dallas > Mathematics (M) > Math 2419 > Differentials Chainr Rule and Directional Derivatives
Saul Cervantes
Accelerated Calculus II
Anotoly Ezlydon

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Accelerated Calculus II
Anotoly Ezlydon
Class Notes
25 ?




Popular in Accelerated Calculus II

Popular in Mathematics (M)

This 3 page Class Notes was uploaded by Saul Cervantes on Monday October 12, 2015. The Class Notes belongs to Math 2419 at University of Texas at Dallas taught by Anotoly Ezlydon in Fall 2015. Since its upload, it has received 44 views. For similar materials see Accelerated Calculus II in Mathematics (M) at University of Texas at Dallas.


Reviews for Differentials, Chainr Rule and Directional Derivatives


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/12/15
DIFFERENTIALS CHAIN RULE AND DIRECTIONAL DERIVATIVES Gradient If f is a function of two or more variables then the gradient of f denoted as V f is the vector composed of the partial derivatives Example fx y z x3y22 then Vf lt 3x2yzz 2x331 zx3y2 gt In other words V f is the derivative of a function of two or more variables Differentiability A function fx y is differentiable at X0 yo if AZ can be written as AzfXAXfyAysl AX82Ay Where 81 82 gt 0 if AX Ay gt 0 Note V f lt AX Ay gt is called a full differential Theorem Suf cient Condition for Differentiability o If f is a function of X and y and fX and fy are continuous in an open region then f is differentiable at this region Theorem 0 If fx y is differentiable at X0 yo then it is continuous at X0 yo Chain Rule Derivative of Composite Function Derivative of Outer Function Derivative of Inner Function Implicit Differentiation Given z fx y and F X y z 0 then 62 Fx az Fy 5 Fz an 5 F2 Directional Derivatives The directional derivative of fX in the direction of u written as DufX is equal to fXtufX 9 Where f is a function of 11 variables X X1 X2 Xn and u is a unit vector u ltu1 u2 ungt


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Allison Fischer University of Alabama

"I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.