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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 first partial derivatives of the function.

35. p = t 4 + u 2 cos   v

To determine

To find: The first order partial derivatives of the function p=t4+u2cosv .

Explanation

Formula used:

If p=f(t,u,v) , then the partial derivative functions are,

ft(t,u,v)=ft=tf(t,u,v)fu(t,u,v)=fu=uf(t,u,v)fv(t,u,v)=fv=vf(t,u,v)

Calculation:

The given function is, p=t4+u2cosv (1)

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

pt=t(t4+u2cosv)=12(t4+u2cosv)12(4t3)=2t3t4+u2cosv

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

pu=u(t4

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