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: 24



Work Step by Step

Take the derivative as is on either side of the equation: $ysecxtanx(dx/dy)+secx=x(secy)^2+(dx/dy)tany$ Move all terms with dx/dy onto one side of the equal sign and distribute the dx/dy out of each term: $dx/dy(ysecxtanx-tany)=x(secy)^2-secx$ Isolate dx/dy by dividing both sides by the terms: $dx/dy=\frac{x(secy)^2-secx}{ysecxtanx-tany}$
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