Answer
$k^{\prime}(x)=2 \tan x \sec^2 x$
Work Step by Step
We have: $k(x)=\tan^2 x$
We need to differentiate both sides with respect to $x$.
$k^{\prime}(x)=2 \tan x \dfrac{d}{dx} [\tan x]\\=2 \tan x \times \sec^2 x\\=2 \tan x \sec^2 x$
Therefore, $k^{\prime}(x)=2 \tan x \sec^2 x$
