Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 12


$$ y' =2t \,sech^2(t^2+1) .$$

Work Step by Step

Since $ y=\tanh (t^2+1)$, then the derivative $ y'$, using the chain rule, is given by $$ y'= sech^2(t^2+1) ( t^2+1)'=2t \,sech^2(t^2+1) .$$
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