Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 122: 27



Work Step by Step

$h(t)=\frac{t}{(t+1)(t^{2}+1)}=\frac{t}{t^{3}+t^{2}+t+1}$ Using the quotient rule, we get $h'(t)=\frac{(t^{3}+t^{2}+t+1)\frac{d}{dt}(t)-t\times\frac{d}{dt}(t^{3}+t^{2}+t+1)}{(t^{3}+t^{2}+t+1)^{2}}$ $=\frac{(t^{3}+t^{2}+t+1)\times1-t(3t^{2}+2t+1)}{(t^{3}+t^{2}+t+1)^{2}}$ $=\frac{-2t^{3}-t^{2}+1}{(t^{3}+t^{2}+t+1)^{2}}$
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