## Calculus (3rd Edition)

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