   Chapter 14.3, Problem 70E

Chapter
Section
Textbook Problem

Find the indicated partial derivative(s).70. u = xaybzc; ∂ 6 u ∂ x   ∂ y 2   ∂ z 3

To determine

To find: The partial derivative 6uxy2z3 of the function u=xaybzc .

Explanation

The given function is, u=xaybzc .

Take the partial derivative of the given function with respect to z and obtain uz .

uz=z(xaybzc)=xaybz(zc)=xayb(czc1)=cxaybzc1

Thus, uz=cxaybzc1 (1)

Take the partial derivative of the equation (1) with respect to z and obtain 2uz2 .

2uz2=z(cxaybzc1)=cxaybz(zc1)=cxayb((c1)zc2)=c(c1)xaybzc2

Hence, 2uz2=c(c1)xaybzc2 (2)

Take the partial derivative of the equation (2) with respect to z and obtain 3uz3 .

3uz3=z(c(c1)xaybzc2)=c(c1)xaybz(zc2)=c(c1)xayb((c2)zc3)=c(c1)(c2)xaybzc3

Thus, 3uz3=c(c1)(c2)xaybzc3 (3)

Take the partial derivative of the equation (3) with respect to y and obtain 4uyz3 .

4uyz3=y(c(c1)(c2)xaybzc3)=c(c1)(c2)xazc3y(yb)=c(c1)(c2)xazc3(byb1)=bc(c1)(c2)xayb1zc3

Hence, 4uyz3=bc(c1)(c2)xayb1zc3 (4)

Take the partial derivative of the equation (4) with respect to y and obtain 5uy2z3

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

On what interval is the curve y=0xt2t2+t+2dt concave downward?

Single Variable Calculus: Early Transcendentals, Volume I

Find y" if x6+y6=1.

Calculus (MindTap Course List)

Find the coordinates of the points that are 10 units away from the origin and have a y-coordinate equal t 6.

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

Suppose . Then F(x)g(x) + C f′(g(x)) + C F(g′(x)) + C F(g(x)) + C

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 