Answer
$y^{\prime}(x)=e^x \sec (e^x) \tan (e^x)$
Work Step by Step
We have: $y(x)= \sec (e^x)$
We differentiate both sides with respect to $x$.
$y^{\prime}(x)=\dfrac{d}{dx} [\sec (e^x)] \\= \sec (e^x) \times \tan (e^x) \times e^x$
Simplify to obtain:
$y^{\prime}(x)=e^x \sec (e^x) \tan (e^x)$
