Activity 10.6.2 Let f(x, y) = 3xy — x²y³. a. Determine f(x, y) and fy(x, y). b. Use Equation (10.6.1) to determine Dif(x, y) and D¡f(x, y). What fa- miliar function is Dif? What familiar function is Djf? (Recall that i is the unit vector in the positive x-direction and j is the unit vector in the positive y-direction.)
Activity 10.6.2 Let f(x, y) = 3xy — x²y³. a. Determine f(x, y) and fy(x, y). b. Use Equation (10.6.1) to determine Dif(x, y) and D¡f(x, y). What fa- miliar function is Dif? What familiar function is Djf? (Recall that i is the unit vector in the positive x-direction and j is the unit vector in the positive y-direction.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.1: Rectangular Coordinate Systems
Problem 8E
Related questions
Question
PLEASE HELP WITH B
![Calculating a directional derivative.
Given a differentiable function f
(u₁, u2), we may compute Duf(x, y) by
=
f(x, y) and a unit vector u
Duf(x, y) = fx(x, y)u1 + fy(x, y)u2.
Activity 10.6.2 Let f(x, y) = 3xy – x²y³.
a. Determine f(x, y) and fy(x, y).
(10.6.1)
b. Use Equation (10.6.1) to determine Dif(x, y) and D¡f(x, y). What fa-
miliar function is Dif? What familiar function is Djf? (Recall that i is
the unit vector in the positive x-direction and j is the unit vector in the
positive y-direction.)
c. Use Equation (10.6.1) to find the derivative of ƒ in the direction of the
vector v = (2,3) at the point (1,-1). Remember that a unit direction
vector is needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feeeb6393-c916-4741-b6e3-3e61715ee264%2Fd2e10664-2758-44aa-85ee-d2bb42b99fea%2Fo5i4nts_processed.png&w=3840&q=75)
Transcribed Image Text:Calculating a directional derivative.
Given a differentiable function f
(u₁, u2), we may compute Duf(x, y) by
=
f(x, y) and a unit vector u
Duf(x, y) = fx(x, y)u1 + fy(x, y)u2.
Activity 10.6.2 Let f(x, y) = 3xy – x²y³.
a. Determine f(x, y) and fy(x, y).
(10.6.1)
b. Use Equation (10.6.1) to determine Dif(x, y) and D¡f(x, y). What fa-
miliar function is Dif? What familiar function is Djf? (Recall that i is
the unit vector in the positive x-direction and j is the unit vector in the
positive y-direction.)
c. Use Equation (10.6.1) to find the derivative of ƒ in the direction of the
vector v = (2,3) at the point (1,-1). Remember that a unit direction
vector is needed.
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