/*! 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. 76 Let聽f(x)聽be聽a聽differentiable... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q. 76 (page 946)

Letf(x)beadifferentiablefunctionofx,g(y)beadifferentiablefunctionofy,andh(x,y)=f(x)g(y).Provethat鈭�2h鈭�x鈭�y=鈭�2h鈭�y鈭�x.

Short Answer

Expert verified

鈭�2h鈭�x鈭�y=鈭�2h鈭�y鈭�x

Step by step solution

01

Step 1. Given information

h(x,y)=f(x)g(y)Where,f(x)isadifferentiablefunctionofx,g(y)isadifferentiablefunctionofy.

02

Step 2. Proof of given partial derivative 

LHS=鈭�2h鈭�x鈭�y=鈭�鈭�x鈭�f(x)g(y)鈭�y=鈭�f(x)g'(y)鈭�x=f'(x)g'(y)RHS=鈭�2h鈭�y鈭�x=鈭�鈭�y鈭�f(x)g(y)鈭�x=鈭�f'(x)g(y)鈭�y=f'(x)g'(y)LHS=RHS

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

Evaluate the following limits, or explain why the limit does not exist.

lim(x,y)鈫�(1,2)x2+y2x2-y2

Find the directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.

f(x,y)=x+yx2+y2,P=(1,2),v=鉄�3,鈭�2鉄�

Evaluate the following limits, or explain why the limit does not exist.

lim(x,y,z)鈫�(1,0,-1)sin(xy)x2-y2+z2

Letf(x)beadifferentiablefunctionofx,g(y)beadifferentiablefunctionofy,andh(x,y)=f(x)+g(y).Provethat鈭�2h鈭�x鈭�y=鈭�2h鈭�y鈭�x.

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.

Explain why(0,0)is not an extremum of f(x,y)=x2ysubject to the constraintx+y=0.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete 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.