Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.6 Directional Derivatives and the Gradient Vector - 14.6 Exercises - Page 997: 7

Answer

a)$\nabla f=\biggl<\dfrac{1}{y}, -\dfrac{x}{y^2}\biggr>$ b)$\nabla f(2, 1)=\bigl<1. -2\bigr>$ c)$-1$

Work Step by Step

For (a) $\nabla f=\biggl<\dfrac{1}{y}, -\dfrac{x}{y^2}\biggr>$ For (b) $\nabla f(2, 1)=\bigl<1. -2\bigr>$ For (c) $\mathbf{D_u}f=\nabla f(2, 1)\cdot \mathbf{u}=\dfrac{3}{5}-\dfrac{8}{5}=-1$
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