Answer
$f'(x)=2x\sec x+(x^2+1)(\sec x\tan x)$
Work Step by Step
$f(x)=(x^2+1)secx$
$f'(x)=\frac{d}{dx}(x^2+1)\times{secx}+(x^2+1)\times{\frac{d}{dx}(secx)}$
$f'(x)=(2x)\times{secx}+(x^2+1)\times{(secxtanx)}$
$f'(x)=2x\sec x+(x^2+1)(\sec x\tan x)$