If $$y = {\cot ^{ - 1}}\left[ {{{\sqrt {1 + \sin x} + \sqrt {1 - \sin x} } \over {\sqrt {1 + \sin x} - \sqrt {1 - \sin x} }}} \right]$$, where $$0 < x < {\pi \over 2}$$, then $${{dy} \over {dx}}$$ is equal to

The function $$f(x) = {{{x^2}} \over {{e^x}}}$$ is monotonically increasing, if

If $${x^a}{y^b} = {(x - y)^{a + b}}$$, then the value of $${{dy} \over {dx}} - {y \over x}$$ is equal to

If $$s = \sqrt {{t^2} + 1} $$, then $${{{d^2}s} \over {d{t^2}}}$$ is equal to