Points of discontinuity of the greatest integer function $f(x) = [x]$, where $[x]$ denotes integer less than or equal to $x$, are

If $y = (log x)^{(log x)}$, $x > 1$ then $\frac{dy}{dx}$ is equal to

If $x = a\sec^3 \theta$, $y = a \tan^3 \theta$, then $\frac{d^2y}{dx^2}$ equals.

If $x = at^2$ and $y = 2at$, then the value of $\frac{d^2y}{dx^2}$ is

( where t is a parameter )

If $x^y = e^{x-y}$, then $\frac{dy}{dx} =$

If $x^2 - y^2 = 1$, then which of the following is correct?

(A) $(x^2 - 1)\left(\frac{dy}{dx}\right)^2 = x^2$

(B) $(x^2 - 1)\left(\frac{d^2y}{dx^2}\right)^2 = x^2$

(C) $(x^2 - 1)^3\left(\frac{d^2y}{dx^2}\right)^2 = x^2$

(D) $(x^2 - 1)^3\left(\frac{d^2y}{dx^2}\right)^2 = 1$

Choose the correct answer from the options given below:

Let $y = \cos(\sin x^2)$, then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{\pi}}{2}$ is equal to