Differentiation

If $f(x) = \cot^{-1}\left(\dfrac{3x - x^3}{1 - 3x^2}\right)$ and $g(x) = \cos^{-1}\left(\dfrac{1 - x^2}{1 + x^2}\right)$, then $\lim\limits_{x \to a}\dfrac{f(x) - f(a)}{g(x) - g(a)}$, $\left(0 < a < \dfrac{1}{2}\right)$ is