Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.5 - Implicit Differentiation - 3.5 Exercises - Page 215: 12



Work Step by Step

Take the derivative as is on either side of the equation: $-sin(xy)\times(x(dy/dx)+y)=0+(dy/dx)cos(y)$ Move all terms with dy/dx onto one side of the equal sign and distribute the dy/dx out of each term: $(dy/dx)\times(cosy+xsin(xy))=-ysin(xy)$ Isolate dy/dx by dividing both sides by the terms: $dy/dx=\frac{-ysin(xy)}{cosy+xsin(xy)}$
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