Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.5 Exercises: 14

Answer

$\dfrac{dy}{dx}=\dfrac{1}{1-\csc^2{y}}.$

Work Step by Step

$\dfrac{d}{dx}(\cot{y})=\dfrac{d}{dx}(x)-\dfrac{d}{dx}(y)\rightarrow$ $\dfrac{dy}{dx}(-\csc^2{y})=1-\dfrac{dy}{dx}\rightarrow$ $1=\dfrac{dy}{dx}(1-\csc^2{y})\rightarrow$ $\dfrac{dy}{dx}=\dfrac{1}{1-\csc^2{y}}.$
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