Select the correct statement from (a), (b), (c), (d). The function $$f(x) = x{e^{1 - x}}$$

The function $$f(x) = {e^{ax}} + {e^{ - ax}},a > 0$$ is monotonically increasing for

The second order derivative of a sin³t with respect to a cos³t at $$t = {\pi \over 4}$$ is

If $$y = {\tan ^{ - 1}}\sqrt {{{1 - \sin x} \over {1 + \sin x}}} $$, then the value of $${{dy} \over {dx}}$$ at $$x = {\pi \over 6}$$ is