Answer
$$ y' =2t \,sech^2(t^2+1)
.$$
Work Step by Step
Since $ y=\tanh (t^2+1)$, then the derivative $ y'$, using the chain rule, is given by
$$ y'= sech^2(t^2+1) ( t^2+1)'=2t \,sech^2(t^2+1)
.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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