Calculus (3rd Edition)

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

Chapter 3 - Differentiation - Chapter Review Exercises - Page 164: 73


$$\frac{dy}{dx}=\frac{\cos(x+y)}{1-\cos(x+y)}, \quad \cos(x+y)\neq 1.$$

Work Step by Step

By differentiating the equation $ y=\sin (x+y)$ with respect to $ x $, we get $$\frac{dy}{dx}=(1+\frac{dy}{dx})\cos(x+y)\\ \Longrightarrow \frac{dy}{dx}(1-\cos(x+y))=\cos(x+y)$$ and hence $$\frac{dy}{dx}=\frac{\cos(x+y)}{1-\cos(x+y)}, \quad \cos(x+y)\neq 1.$$
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