If $$y = \sin \left( {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right)$$, then $${{dy} \over {dx}}$$ is :

Let f(x) be a polynomial function of second degree. If f(1) = f($$-$$1) and a, b, c are in AP, then f'(a), f'(b) and f'(c) are in.

Given that $$f(x) = 2{x^3} + {x^4} + \log x$$ and assuming g to be the inverse function of f, compute the value of g'(3).