Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - Review - Exercises: 24

Answer

$2x\sin \left( 1+x^{2}\right) sec\left( 1+x^{2}\right) $

Work Step by Step

$y=sec\left( 1+x^{2}\right) =\dfrac {1}{\cos \left( 1+x^{2}\right) }\Rightarrow y'=\dfrac {\sin \left( 1+x^{2}\right) }{\cos ^{2}\left( 1+x^{2}\right) }\times \left( \dfrac {d}{dx}\left( 1+x^{2}\right) \right) =2x\dfrac {\sin \left( 1+x^{2}\right) }{\cos ^{2}\left( 1+x^{2}\right) }=2x\sin \left( 1+x^{2}\right) sec\left( 1+x^{2}\right) $
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