The derivative of ^ - 1 (( x - x)/( x + x)) with respect to...

Given function can be written as

$y = \tan^{- 1}\left(\dfrac{\sin x - \cos x}{\sin x + \cos x}\right)$

$⇒ y = \tan^{- 1}\left(\dfrac{\tan x - 1}{\tan x + 1}\right)$

$⇒ y = \tan^{- 1}\left(\tan \left(x - \dfrac{\pi}{4}\right)\right)\left(givenx \in \left(0, \dfrac{\pi}{2}\right)\right)$
$⇒ y = x - \dfrac{\pi}{4}$
Now $\dfrac{dy}{d\left(\dfrac{x}{2}\right)} = 2\dfrac{dy}{dx} = 2$