Calculus 8th Edition

Published by Cengage

Chapter 14 - Partial Derivatives - 14.6 Directional Derivatives and the Gradient Vector - 14.6 Exercises - Page 998: 35

Answer

$\dfrac{327}{13}$

Work Step by Step

Our aim is to determine the direction derivative of $f(x,y)$.In order to find this, we have : $D_uf=|\nabla f(x,y)|$ or, $D_uf=\nabla f(x,y) \cdot u$ From the given data ion the question, we have $f_x(1,3)=3 , f_y(1,3)=26$ This implies $D_uf=\nabla f(x,y) \cdot u$ or, $D_uf(1,3)=f_x(1,3)(\dfrac{5}{13})+f_y(1,3)(\dfrac{12}{13})$ Thus,$D_uf(1,3)=3(\dfrac{5}{13})+26(\dfrac{12}{13})$ $D_uf(1,3)=\dfrac{327}{13}$

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