Answer
$y'=8\sec^2{x}\tan{x}.$
Work Step by Step
Using the Chain Rule:
$u=\sec{x}$; $\dfrac{du}{dx}=\sec{x}\tan{x}$
$y=4u^2 ;\dfrac{dy}{du}=8u$
$\dfrac{dy}{dx}=\dfrac{dy}{du}\times\dfrac{du}{dx}=(8\sec{x})(\sec{x}\tan{x})=8\sec^2{x}\tan{x}.$
