If $$2y = {\left( {{{\cot }^{ - 1}}\left( {{{\sqrt 3 \cos x + \sin x} \over {\cos x - \sqrt 3 \sin x}}} \right)} \right)^2}$$,

x $$ \in $$ $$\left( {0,{\pi \over 2}} \right)$$ then $$dy \over dx$$ is equal to:

For x > 1, if (2x)^2y = 4e^2x$$-$$2y,

then (1 + log_e 2x)² $${{dy} \over {dx}}$$ is equal to :

If  xlog_e(log_ex) $$-$$ x² + y² = 4(y > 0), then $${{dy} \over {dx}}$$ at x = e is equal to :

Let f : R $$ \to $$ R be a function such that f(x) = x³ + x²f'(1) + xf''(2) + f'''(3), x $$ \in $$ R. Then f(2) equals -