/*! 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 71. Prove that鈭�(f(x,y)g(x,y))=f(x,... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q 71. (page 965)

Prove that

鈭�(f(x,y)g(x,y))=f(x,y)鈭�g(x,y)+g(x,y)鈭�f(x,y)

Short Answer

Expert verified

The above relation can be proved using the formula

鈭�(f(x,y)g(x,y))=i鈭�(f(x,y)g(x,y))鈭�x+j鈭�(f(x,y)g(x,y))鈭�y

Step by step solution

01

Given Information

Considering f(x,y),g(x,y)

We need to show that

鈭�(f(x,y)g(x,y))=f(x,y)鈭�g(x,y)+g(x,y)鈭�f(x,y)

02

Simplification

Simplifying for 鈭�(f(x,y)g(x,y))=i鈭�(f(x,y)g(x,y))鈭�x+j鈭�(f(x,y)g(x,y))鈭�y

鈭�(f(x,y)g(x,y))=if(x,y)鈭�g(x,y)+g(x,y)鈭�f(x,y)鈭�x+jf(x,y)鈭�g(x,y)+g(x,y)鈭�f(x,y)鈭�y

鈭�(f(x,y)g(x,y))=f(x,y)i鈭�g鈭�x+j鈭�g鈭�y+g(x,y)i鈭�f鈭�x+j鈭�f鈭�y

鈭�(f(x,y)g(x,y))=f(x,y)鈭�(g(x,y))+g(x,y)鈭�(f(x,y))

Hence proved.

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 37-42, use the partial derivatives of fx,y=xsinyand the point 2,蟺3specified to

afind the equation of the line tangent to the surface defined by the function in the xdirection,

bfind the equation of the line tangent to the surface defined by the function in the ydirection, and

cfind the equation of the plane containing the lines you found in parts aand b.

ThepressurePofanidealgasisgivenbyP(n,T,V)=nRTV,wherenistheamountofthegas,Risaconstant,TisthetemperatureofthegasindegreesKelvin,andVisthevolumeofthegas.Find鈭�P鈭�n,鈭�P鈭�V,and鈭�P鈭�T.Whatarethephysicalinterpretationsofthesepartialderivatives?

Use Theorem 12.32 to find the indicated derivatives in Exercises 21鈥�26. Express your answers as functions of a single variable.

drdtwhenr=x2+y2,x=tandy=t2

Explain how you could use the method of Lagrange multipliers to find the extrema of a function of two variables, f(x,y),subject to the constraint that (x,y)is a point on the boundary of a triangle Tin the xy-plane.

Gradients: Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

f(x, y ,z) = ln(x + y + z), P = (e, 0, 鈭�1) .
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

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.