Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the unit vector u = cos i + sin 0 j. f(x, y) = 8x + y P(2,0), 8 = TT : 160

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 32E
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Theorem 13.9 Directional Derivative
If f is a differentiable function of x and y, then the directional derivative of f in the direction of the
unit vector u = cos i + sin oj is
Duf(x, y) = f (x, y) cos 0 + fy (x, y) sin 0.
Transcribed Image Text:Theorem 13.9 Directional Derivative If f is a differentiable function of x and y, then the directional derivative of f in the direction of the unit vector u = cos i + sin oj is Duf(x, y) = f (x, y) cos 0 + fy (x, y) sin 0.
Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the unit vector u = cos i + sin 0j.
y
3x + y² P(2, 0),
TU
6
8x
f(x, y) =
8=-
Transcribed Image Text:Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the unit vector u = cos i + sin 0j. y 3x + y² P(2, 0), TU 6 8x f(x, y) = 8=-
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