Answered: Activity 10.6.2 Let f(x, y) = 3xy —… | bartleby

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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PLEASE HELP WITH B. IT WOULD BE GREAT IF YOU'RE WILLING TO DO C, BUT DEFINITELY 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.

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