Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Review - True-False Quiz: 9

Answer

False

Work Step by Step

As per the definition of a gradient vector $∇f(x,y)=f_{x}i+f_{y}j$ Therefore, $∇f(x,y)=∇(lny)=\frac{∂(lny)}{∂x}i+\frac{∂(lny)}{∂y}j$ $=\frac{1}{y}j$ Thus, $∇f(x,y)=\frac{1}{y}j$ Hence, $∇f(x,y) \ne \frac{1}{y}$
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