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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the indicated partial derivative(s).

68. V = ln(r + s2 + t3); 3 V r   s   t

To determine

To find: The derivative 3Vrst of the function V=ln(r+s2+t3) .

Explanation

The given function is, V=ln(r+s2+t3) .

Take the partial derivative of the given function with respect to t and obtain Vt .

Vt=t(ln(r+s2+t3))=t(ln(r+s2+t3))t(r+s2+t3)=1r+s2+t3(0+0+3t2)=3t2r+s2+t3

Thus, Vt=3t2r+s2+t3 (1)

Take the partial derivative of the equation (1) with respect to s and obtain, 2Vst .

2Vst=s(3t2r+s2+t3)=3t2s(1r+s2+t3)=3t2[(1)(r+s2+t3)2(2s)]=6st2(r+s2+t3

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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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