Calculus: Early Transcendentals 8th Edition

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

Chapter 14 - Section 14.5 - The Chain Rule. - 14.5 Exercise - Page 944: 28


$-\dfrac{y \sin xy}{x \sin xy+\cos y}$

Work Step by Step

Recall Equation 6: $\dfrac{dy}{dx}=-\dfrac{F_x}{F_y}$ ...(1) Given: $ \cos x=1+\sin y$ Consider that $F(x,y)=\cos (xy)=1-\sin y=0$ $F_x=-y \sin xy\\F_y= -x \sin (xy) -\cos y$ Equation (1) becomes: $\dfrac{dy}{dx}=-\dfrac{-y \sin xy}{-x \sin (xy) -\cos y}=-\dfrac{y \sin xy}{x \sin xy+\cos y}$
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