Answer
$$y'=2\tan x$$
Work Step by Step
Given $$y=\ln\left(sec^{2\:}x\right)$$
Then
\begin{align*}
y'&=\frac{1}{\sec ^2\left(x\right)}\cdot \:2\sec ^2\left(x\right)\tan \left(x\right)\\
&=2\tan x
\end{align*}
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