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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 first partial derivatives of the function.

37. h(x, y, z, t) = x2y cos(z/t)

To determine

To find: The first order partial derivatives of the function h(x,y,z,t)=x2ycos(zt) .

Explanation

Formula used:

If h=f(x,y,z,t) , then the partial derivative functions are,

fx(x,y,z,t)=fx=xf(x,y,z,t)fy(x,y,z,t)=fy=yf(x,y,z,t)fz(x,y,z,t)=fz=zf(x,y,z,t)ft(x,y,z,t)=ft=tf(x,y,z,t)

Calculation:

The given function is, h(x,y,z,t)=x2ycos(zt) (1)

Take the partial derivative with respect to x for the equation (1),

hx=x(h(x,y,z,t))=x(x2ycos(zt))=ycos(zt)(2x)=2xycos(zt)

Take the partial derivative with respect to y for the equation (1),

hy=y(h(x,y,z,t))=y(x2ycos(zt))=x2cos(<

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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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