Calculus 8th Edition

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

Chapter 14 - Partial Derivatives - Review - Exercises - Page 1024: 45



Work Step by Step

Our aim is to determine the directional derivative. In order to find it we have to use the expression: $D_uf(x,y)=f_x(x,y)m+f_y(x,y)n$ Given: $f(x,y)=x^2e^{-y}; (-2,0)$ and in the direction towards the point $(2,-3)$ $D_uf(x,y)=2xe^{-y}\dfrac{4}{5}-x^2e^{-y}\dfrac{-3}{5}$ This implies From the given data, we have : $(x,y)=$ $(-2,0)$ $D_uf(0,1)=2(-2)e^{0}\dfrac{4}{5}-(-2)^2e^{0}\dfrac{-3}{5}=-\dfrac{4}{5}$
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