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Activity 10.6.2 Let f(x, y) = 3xy – x²y³. a. Determine fx (x, y) and fy(x, y).

Activity 10.6.2 Let f(x, y) = 3xy – x²y³. a. Determine fx (x, y) and fy(x, y).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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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.
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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