Answer
$-1$
Work Step by Step
$$1-x-y^{2}-\sin(x \ y)=0 \\ -dx-2y \ dy-\cos(xy)\ y \ dx-\ cos(xy) \ x\ dy=0 $$
When $x=0,y=1 $, then we have:
$$-dx-2dy-dx=0 \\-2dx =2dy\\ \dfrac{dy}{dx}=-1$$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 13 - Practice Exercises - Page 750: 35
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