Answer
$\dfrac{d}{dx}( \sec x)= \sec x \tan x$
Work Step by Step
Need to prove $\dfrac{d}{dx}( \sec x)= \sec x \tan x$
Consider left hand side.
$\dfrac{d}{dx}( \sec x)=\dfrac{d}{dx}( \dfrac{1}{\cos x})\\=\dfrac{ \sin x}{ \cos^2 x}\\=(\dfrac{1}{\cos x})(\dfrac{\sin x}{\cos x})\\= \sec x \tan x$
