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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
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

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Chapter 14 Solutions

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P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-58RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8P

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