If f(x) = sin-1 $\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),$ then f'$\left( { - {1 \over 2}} \right)$ equals :

Question

If f(x) = sin^-1 $\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),$ then f'$\left( { - {1 \over 2}} \right)$ equals :

$ - \sqrt 3 {\log _e}\sqrt 3 $

$ \sqrt 3 {\log _e}\sqrt 3 $

$ - \sqrt 3 {\log _e}\, 3 $

$ \sqrt 3 {\log _e}\, 3 $

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