Differentiate `tan^(-1)((a+x)/(1-a x))` with respect to `x`

Explanation

Solution:

`\tan ^{-1}((a+x) /(1-a x))`

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

Putting `a=\tan \alpha and x=\tan \theta`

Diff. w.r.t. x,

Therefore, `\quad \frac{d y}{d x}=\frac{1}{1+x^{2}}`