Differentiate `tan^(-1)(tanx),\ \ x in [0,\ pi]-{pi/2}`

Explanation

Given that,
`y=tan^(-1)(tanx),\ \ x in [0,\ pi]-{pi/2}`
`tan^(-1)(tanx)={{:(x, 0 le x lt pi/2),(x-pi , pi/2 lt x le pi):}`
`y'={{:(1, 0 le x lt pi/2),(1 , pi/2 lt x le pi):}`
so,
`(dy)/(dx)=1`