If `y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0.` Find `(dy)/(dx)dot`

Explanation

We have, `{y}=sec ^{-1}(frac{x+1}{x-1})+sin ^{-1}(frac{x-1}{x+1})`


`Rightarrow y=cos ^{-1}(frac{x-1}{x+1})+sin ^{-1}(frac{x-1}{x+1}) cdots cdots cdots[because sec ^{-1} x=cos ^{-1}(frac{1}{x})] `

`Rightarrow y=frac{pi}{2} ldots cdots cdot[because sin ^{-1} x+cos ^{-1} x=frac{pi}{2}] `

`Rightarrow frac{d y}{d x}=0`