   Chapter 14.6, Problem 6E

Chapter
Section
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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