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) $
