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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 f at the given point in the direction indicated by the angle θ.

6. f(x, y) = 2 x + 3 y , (3, 1), θ = −π/6

To determine

To find: The directional derivative of the function f(x,y)=2x+3y at the point (3,1) in the direction of the angle θ=π6 .

Explanation

Given:

The functionis f(x,y)=2x+3y .

Result used:

“The directional derivative of the function f(x,y) at f(x0,y0) in the direction of the angle θ is Duf(x,y)=fx(x,y)cosθ+fy(x,y)sinθ .”

Calculation:

Substitute the respective values in Duf(x,y) and obtain its value as follows,

Duf(x,y)=fx(x,y)cosθ+fy(x,y)sinθ=x(2x+3y)cos(π6)+y(2x+3y)sin(π6)=(222x+3y)(32)+(322x+3y)(12)=(12x+3y)(32)(322x+3y)(12)

Thus, the directional derivative of f(x,y)</

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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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