Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.8 Implicit Differentiation - Exercises - Page 152: 21


$\frac{dy}{dx}=\frac{1-\cos(x+y)}{\cos (x+y)+\sin y}$

Work Step by Step

Implicitly differentiate $\sin (x+y)=x+\cos y$ with respect to $x$: $[\cos (x+y)](1+\frac{dy}{dx})=1+(-\sin y\times \frac{dy}{dx})$ Or $\cos(x+y)+\cos (x+y)\frac{dy}{dx}=1-\sin y \times\frac{dy}{dx}$ $\implies cos(x+y)\frac{dy}{dx}+\sin y\frac{dy}{dx}$$=1-\cos (x+y)$ Or $\frac{dy}{dx}=\frac{1-\cos(x+y)}{\cos (x+y)+\sin y}$
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