Differentiate the following function with respect to `x :` `tan^(-1)((a+x)/(1-a x))`

Explanation

Let `y=tan ^{-1}(frac{a+x}{1-a x})`

`Rightarrow y=tan ^{-1} a+tan ^{-1} x[text { Since }, tan ^{-1} x+tan ^{-1} y=tan ^{-1}(frac{x+y}{1-x y})]`

`frac{d y}{d x}=frac{d}{d x}(tan ^{-1} a)+frac{d}{d x}(tan ^{-1} x) `

`Rightarrow frac{d y}{d x}=0+frac{1}{1+x^{2}} `

`therefore frac{d y}{d x}=frac{1}{1+x^{2}}`