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

Explanation

Suppose `u=\tan ^{-1}(1+a x) /(1-a x) and v=\sqrt{(1+a^{2} x^{2})}`



To differentiate `u` with respect to `v `to find `du / dv`


On substituting a `x=\tan \theta` in `u`


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