Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 13 - Functions of Several Variables - 13.6 Exercises - Page 924: 5

Answer

$1$

Work Step by Step

The directional derivative of f where f is a function of x and y is denoted by $D_{u}f(x,y)$ and is found by the formula: $D_{u}f(x,y)=f_{x}(x,y)cosB+f_{y}(x,y)sinB$ Where $cosB$ and $sinB$ are found from the directional unit vector $u=cosBi+sinBj$ $f(x,y)=3x-4xy+9y$ Our directional unit vector is given. $v=\frac{3}{5}i+\frac{4}{5}j$ In this case, $cosB=3/5$ and $sinB=4/5$ Now we use the formula to find the directional derivative. $D_{u}f(x,y)=(3-4y)(3/5)+(-4x+9)(4/5)$ Substituting in the point $(1,2)$ we have $D_{u}f(1,2)=(3-4(2))(3/5)+(-4(1)+9)(4/5)$ $=1$
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