Calculus 10th Edition

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

Chapter 2 - Differentiation - 2.4 Exercises: 20

Answer

$y'=\dfrac{12}{(t-2)^5}$

Work Step by Step

$y=-\dfrac{3}{(t-2)^4}=-3(t-2)^{-4}.$ Using the Chain Rule: $u=(t-2)$; $\dfrac{du}{dt}=1$ $\dfrac{dy}{du}=\dfrac{12}{u^5}$ $\dfrac{dy}{dt}=\dfrac{dy}{du}\times\dfrac{du}{dt}=\dfrac{12}{(t-2)^5}.$
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