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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 directional derivative of the function at the given point in the direction of the vector v.

13. g(s, t) = s t , (2, 4), v = 2ij

To determine

To find: The directional derivative of the function g(s,t)=st at the point (2,4) in the direction of the vector v=2ij .

Explanation

Result used:

“The directional derivative of the function f(x,y,z) at f(x0,y0,z0) in the direction of unit vector u=a,b,c is Duf(x,y,z)=f(x,y,z)u , where f(x,y,z)=fx,fy,fz=fxi+fyj+fzk .”

Calculation:

The given function is g(s,t)=st .

The directional derivative is defined as, Dug(x,y,z)=g(x,y,z)u . (1)

The value of g(s,t) is computed as follows,

g(s,t)=gs,gt=s(st),t(st)=(1(t)),(s(1t))=(t),(st)

Thus, the value of g(s,t)=(t),(st)

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Chapter 14 Solutions

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