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 -

If   x $$=$$ 3 tan t and y $$=$$ 3 sec t, then the value of $${{{d^2}y} \over {d{x^2}}}$$ at t $$ = {\pi \over 4},$$ is :