/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 35 In Exercises 35鈥�38, find the d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q. 35 (page 953)

In Exercises 35鈥�38, find the directional derivative of the given

function at the specified point P and in the direction of the

given vector v.

f(x,y)=x2鈭�y2atP=(3,3),v=-1,5

Short Answer

Expert verified

The directional derivative of the given

function is鈭�181326

Step by step solution

01

Given data

f(x,y)=x2鈭�y2

P=x0,y0=(3,3)andy=(鈭�1,5)

02

solution

Therefore

鈭�v鈭�=鈭�12+52=26

u=(伪,尾)=鈭�2626,52626

Directional derivation function at Ppoint is given by

鈭�f(P)脳u=鈭�f(3,3)脳u=dfdx(3,3)i+dfdy(3,3)j脳鈭�2626i+52626j

=(2x)(3,3)i+(鈭�2y)(3,3)j鈰�鈭�2626i+52626j

=(6i鈭�6j)脳鈭�2626i+52626j

=鈭�62626鈭�302626

=鈭�362626

鈭�f(P)鈰�u=鈭�181326

鈭�f(P)鈰�u=鈭�181326

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises, by considering the function f(x,y)=x2ysubject to the constraint x+y=0,you will explore a situation in which the method of Lagrange multipliers does not provide an extremum of a function.

Why does the method of Lagrange multipliers fail with this function?

Describe the meanings of each of the following mathematical expressions:

fzx0,y0,z0

Explain the steps you would take to find the extrema of a function of two variablesf(x,y),if (x,y)is a point in a triangle role="math" localid="1649884242530" Tin the xy-plane.

Use Theorem 12.33 to find the indicated derivatives in Exercises 27鈥�30. Express your answers as functions of two variables.

鈭�z鈭�rwhenz=(x2+xy)ey,x=rcos胃andy=rsin胃

Use Theorem 12.33 to find the indicated derivatives in Exercises 27鈥�30. Express your answers as functions of two variables.

鈭�z鈭�swhenz=x2y3,x=tsins,andy=scost
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.