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 216: 37



Work Step by Step

Find y' by taking the derivative of both sides of the equation: $cosy\times y'-sinx=0$ $y'=\frac{sinx}{cosy}$ Find y": $y"=\frac{(cosy)(cosx)-(sinx)(-siny\times y')}{cos^2y}$ Plug y' into y": $y"=\frac{cosxcosy+sinxsiny\times\frac{sinx}{cosy}}{cos^2y}$ Simplify: $y"=\frac{cosxcos^2y+sin^2xsiny}{cos^3y}$
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