Differentiate `tan^(-1)((1-x)/(1+x))` with respect to `sqrt(1-x^2)` , if `-1 < x < 1` .

Explanation

` text{ Let, } u=tan ^{-1}(frac{1-x}{1+x})`

`text { Put } x=tan theta`

`Rightarrow theta=tan ^{-1} x`

`Rightarrow u=tan ^{-1}(frac{1-tan theta}{1+tan theta})`

`Rightarrow u=tan ^{-1}[tan (frac{pi}{4}-theta)] ldots(i)`

`text { Here, }`

`-1 < x < 1`

`Rightarrow-1 < tan theta < 1`

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