×

### Let's log you in.

or

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

×

or

## Differentials, Chainr Rule and Directional Derivatives

1 review
by: Saul Cervantes

49

1

3

# 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
UTD
Accelerated Calculus II
Anotoly Ezlydon

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

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

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

×
Unlock Preview

COURSE
Accelerated Calculus II
PROF.
Anotoly Ezlydon
TYPE
Class Notes
PAGES
3
WORDS
KARMA
25 ?

1 review
Evan Mcgregor

## 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 49 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

-Evan Mcgregor

×

×

### What is Karma?

#### 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

×

×

### BOOM! Enjoy Your Free Notes!

×

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

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."

Jennifer McGill UCSF Med School

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over \$500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

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."

Parker Thompson 500 Startups

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION 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 support@studysoup.com

#### STUDYSOUP REFUND POLICY

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: support@studysoup.com

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 support@studysoup.com