University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Practice Exercises - Page 202: 29



Work Step by Step

Given that $s=(\dfrac{4t}{t+1})^{-2}$ Apply derivative rules of differentiation: $f(x)/g(x)=\dfrac{p'(x)q(x)-p(x)q'(x)}{g(x))^2}$ $s'=\dfrac{d}{dx}[(\dfrac{4t}{t+1})^{-2}]$ $=-2(\dfrac{4t}{t+1})^{-3}\dfrac{d}{dx}(\dfrac{4t}{t+1})$ $=-2(\dfrac{4t}{t+1})^{-3}[\dfrac{4t+4-4t}{(t+1)^2}]$ Hence, $s'=-2(\dfrac{4t}{t+1})^{-3}[\dfrac{4}{(t+1)^2}]$
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