The value of $${{dy} \over {dx}}$$ at $$x = {\pi \over 2}$$, where y is given by $$y = {x^{\sin x}} + \sqrt x $$ is

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