JEE Math Practice Question

The derivative of $${\tan ^{ - 1}}\left( {{{\sqrt {1 + {x^2}} - 1} \over x}} \right)$$ with respect to $${\tan ^{ - 1}}\left( {{{2x\sqrt {1 - {x^2}} } \over {1 - 2{x^2}}}} \right)$$ at x = $${1 \over 2}$$ is :

1. A.$${{2\sqrt 3 } \over 3}$$
2. B.$${{2\sqrt 3 } \over 5}$$
3. C.$${{\sqrt 3 } \over {10}}$$
4. D.$${{\sqrt 3 } \over {12}}$$