Calculus 10th Edition

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

Chapter 2 - Differentiation - 2.6 Exercises: 6

Answer

a) $\frac{dy}{dt} = \frac{24}{25} $ in/sec b) $\frac{dy}{dt} = 0 $ in/sec c) $\frac{dy}{dt} = -\frac{24}{25} $ in/sec

Work Step by Step

y = $\frac{1}{1+x^2}$ $\frac{dy}{dt} = -(1+x^2)^-2*(2x) \frac{dx}{dt} = \frac{-2x}{(1+x^2)^2} \frac{dx}{dt}$ when dx/dt = 6 in/sec a) x = -2 $\frac{dy}{dt} = \frac{-2(-2)}{(1+(-2)^2)^2}(6) = \frac{24}{25}$ b)x = 0 $\frac{dy}{dt} = \frac{-2(0)}{(1+(0)^2)^2}(6) = 0$ c) x = 2 $\frac{dy}{dt} = \frac{-2(2)}{(1+(2)^2)^2}(6) =- \frac{24}{25}$
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