If $$x = {e^t}\sin t$$, $$y = {e^t}\cos t$$ then $${{{d^2}y} \over {d{x^2}}}$$ at x = $$\pi$$ is

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