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: 35

Answer

$y=-x+2.$

Work Step by Step

$\dfrac{d}{dx}(xy)=\dfrac{d}{dx}(1)\rightarrow$ $y+\dfrac{dy}{dx}(x)=0\rightarrow\dfrac{dy}{dx}=-\dfrac{y}{x}.$ At $(1, 1)\rightarrow\dfrac{dy}{dx}=-\dfrac{1}{1}=-1.$ Equation of tangent: $(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$. $(y-1)=-(x-1)\rightarrow y=-x+2.$
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