Answer
$$ f'(x)
=\frac{2\sec^2 x}{(1-\tan x)^2} .$$
Work Step by Step
Since $ f(x)= \frac{1+\tan x}{1-\tan x}$, then using the quotient rule, the derivative is giving by
$$ f'(x)=\frac{(1-\tan x)(\sec^2x)- (1+\tan x)(-\sec^2x)}{(1-\tan x)^2} \\
=\frac{2\sec^2 x}{(1-\tan x)^2} .$$
