The function f(x)=tan ^-1(tan x), is

The graph of the function $f(x)=\tan ^{-1}(\tan x)$ is as given in Figure.

It is evident from the curve y = f(x) that f(x) is discontinuous and hence non-differentiable at $x=(2 n+1) \frac{\pi}{2}, n \in Z$ such that f'(x) = 1 for all $x \in R-\left\{(2 n+1) \frac{\pi}{2}, n \in Z\right\}$.