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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 gradient vector field of f.

22. f(s, t) = 2 s + 3 t

To determine

To find: The gradient vector field for equation f(s,t)=2s+3t .

Explanation

Given data:

f(s,t)=2s+3t

Formula used:

Write the expression for gradient vector field of two dimensional vector.

f(x,y)=fxi+fyj (1)

Write the required differentiation formulae as follows.

x[x]=12x

Differentiate terms with respect to s .

s2s+3t=122s+3ts(2s)=122s+3t(2)s(s)=122s+3t(2)(1)=12s+3t

Differentiate terms with respect to t .

t2s+3t=122s+3tt(3t)=122s+3t(t

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Chapter 16 Solutions

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