Answer
$2x\tan \left( 1+x^{2}\right) sec\left( 1+x^{2}\right) $
Work Step by Step
$\dfrac {d}{dx}sec\left( 1+x^{2}\right) =sec\left( 1+x^{2}\right) \times \tan \left( 1+x^{2}\right) \times \dfrac {d}{dx}\left( 1+x^{2}\right) =2x\tan \left( 1+x^{2}\right) sec\left( 1+x^{2}\right) $
