University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 3 - Section 3.3 - Differentiation Rules - Exercises - Page 136: 21



Work Step by Step

$$v=(1-t)(1+t^2)^{-1}=\frac{1-t}{1+t^2}$$ Apply the Derivative Quotient Rule, we have $$v'=\frac{(1-t)'(1+t^2)-(1-t)(1+t^2)'}{(1+t^2)^2}$$ $$v'=\frac{(0-1)(1+t^2)-(1-t)(0+2t)}{(1+t^2)^2}$$ $$v'=\frac{-(1+t^2)-(1-t)\times2t}{(1+t^2)^2}$$ $$v'=\frac{-1-t^2-(2t-2t^2)}{(1+t^2)^2}$$ $$v'=\frac{-1-t^2-2t+2t^2}{(1+t^2)^2}$$ $$v'=\frac{t^2-2t-1}{(1+t^2)^2}$$
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