   Chapter 15.9, Problem 6E

Chapter
Section
Textbook Problem

Find the Jacobian of the transformation.6. x = u + vw, y = v + wu, z = w + uv

To determine

To find: Jacobian transformation of x=u+vw, y=v+wu and z=w+uv.

Explanation

Definition used: Jacobian transformation

The Jacobian of the transformation T given by x=g(u,v), y=h(u,v) and z=k(u,v) is

(x,y,z)(u,v,w)=|xuxvxwyuyvywzuzvzw|=xu(yvzwywzv)xv(yuzwywzu)+xw(yuzvyvzu)

Calculation:

Given that, x=u+vw

Take partial derivative of x with respect to u to obtain xu.

xu=1+01

Take partial derivative of x with respect to v to obtain xv.

xv=0+(1)w=w

Take partial derivative of x with respect to w to obtain xw.

xw=0+v(1)=v

Given that, y=v+wu

Take partial derivative of y with respect to u to obtain yu.

yu=0+w(1)=w

Take partial derivative of y with respect to v to obtain yv

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 5-8, graph the given function or equation. 2x3y=12

Finite Mathematics and Applied Calculus (MindTap Course List)

f(x)1x(x+2)(x3)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

The third partial sum of is:

Study Guide for Stewart's Multivariable Calculus, 8th 