Answer
$\sec x \tan x$
Work Step by Step
Let we have: $z(x)= \sec x$
Use reciprocal identity $\sec x=\dfrac{1}{\cos x}$
We differentiate both sides with respect to $x$.
$z^{\prime}(x)=\dfrac{d}{dx} [ 1/\cos x] \\=-(\cos x)^{-2} \times (-\sin x)$
Simplify to obtain:
$z^{\prime}(x)=\dfrac{1}{\cos x} \times (\dfrac{\sin x}{\cos x}) =\sec x \tan x$
