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: 28


$\dfrac{dy}{dx}=\dfrac{\cot{y}}{x}.$ At $(2, \dfrac{\pi}{3})\rightarrow\dfrac{dy}{dx}=\dfrac{\cot{\dfrac{\pi}{3}}}{2}=\dfrac{\sqrt{3}}{6}.$

Work Step by Step

$\dfrac{d}{dx}(x\cos{y})=\dfrac{d}{dx}(1)\rightarrow$ $(\cos{y}-\dfrac{dy}{dx}(x\sin{y}))=0\rightarrow$ $\dfrac{dy}{dx}=\dfrac{\cot{y}}{x}.$ At $(2, \dfrac{\pi}{3})\rightarrow\dfrac{dy}{dx}=\dfrac{\cot{\dfrac{\pi}{3}}}{2}=\dfrac{\sqrt{3}}{6}.$
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