If $y = \sqrt{x + \sqrt{x^2 + 1}}$, then the value of $\dfrac{dy}{dx}$ is

If $y = \sin(e^{\log 2x})$, then the value of $\dfrac{dy}{dx}$ at $x = \dfrac{\pi}{2}$ is

The difference between the local extreme values of the function $f(x) = 2x^3 - 15x^2 + 36x + 40$ is ......

A wire of length $64$ m is to be bent to form a rectangle such that its area is maximum, then its area is.....