Answered: Let f(x, y) = arctan(xy). Find the unit…

Let f(x, y) = arctan(xy). Find the unit vector in the direction where the directional derivative of f at (1, 2) is maximum. What is the maximum rate of change at (1, 2

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.1: Techniques For Finding Derivatives

Problem 25E: Explain the relationship between the slope and the derivative of fx at x=a.

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Question

Let f(x, y) = arctan(xy). Find the unit vector in the direction where the directional derivative of f at (1, 2) is maximum. What is the maximum rate of change at (1, 2)?

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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