If $y = \log(\log x)$, then $\frac{d^2y}{dx^2}$ is equal to: (Consider $\log_e x = \log x$)

If $x = a\left(\cos t + \log \tan\frac{t}{2}\right), y = a\sin t$, then value of $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$ is

If $x=t^3, y=t^4$, then $\frac{d^2y}{dx^2}$ is:

If $x\sqrt{1+y}+y\sqrt{1+x}=0, x>-1$ and $x\neq y$, then $(1+x)^2\frac{dy}{dx}$ is equal to

If $y=\frac{\log x}{x}$, then $\frac{d^2y}{dx^2}$ is equal to(Consider $\log_e x = \log x$):

The function $f(x) = \frac{x-1}{x(x^2-1)}, x \neq 1, f(1) = 1$, is discontinuous at

If a function $f(x) = \begin{cases}\lambda(x^2-2x), & x \le 0\\4x+1, & x>0\end{cases}$ then