Calculate the directional derivative of f(x, y) = cot=1(xy) in the direction of v = 2i +j at the point P = (0.5, 0.5). Remember to normalize the direction vector. Duf(0.5, 0.5)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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Answer both questions. Thank you.

Calculate the directional derivative of f(x, y)
cot(xy) in the direction of v = 2i +j at the point P = (0.5, 0.5). Remember to normalize
the direction vector.
Duf(0.5,0.5)
Transcribed Image Text:Calculate the directional derivative of f(x, y) cot(xy) in the direction of v = 2i +j at the point P = (0.5, 0.5). Remember to normalize the direction vector. Duf(0.5,0.5)
Let f(æ, y) = xe-y and P = (1,1).
(a) Calculate || Vfp||-
2
(b) Find the rate of change of ƒ in the direction Vfp.
(c) Find the rate of change of f in the direction of a vector making an angle of 45° with Vƒp.
Answers :
(а)
(b)
(c)
Transcribed Image Text:Let f(æ, y) = xe-y and P = (1,1). (a) Calculate || Vfp||- 2 (b) Find the rate of change of ƒ in the direction Vfp. (c) Find the rate of change of f in the direction of a vector making an angle of 45° with Vƒp. Answers : (а) (b) (c)
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