If $y=(\sqrt x)^\pi$ such that $\frac{dy}{dx}=\frac{\pi}{a}y^{\pi+b}$ where $a,b\in\mathbb R$ then:

If $y = \frac{1}{1+x^{b-a}+x^{c-a}} + \frac{1}{1+x^{c-b}+x^{a-b}} + \frac{1}{1+x^{a-c}+x^{b-c}}$ then $\frac{d^2y}{dx^2}$ is

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

Match List-I with List-II

Choose the correct answer from the options given below:

If $y = x\log_e\left(\dfrac{x}{2+x}\right)$, then $x^3\dfrac{d^2y}{dx^2}$ is equal to:

The point('s) at which the function $f$ given by $f(x) = \begin{cases} \dfrac{|x|}{2x}, & x<0 \\ -\dfrac{1}{2}, & x\geq0 \end{cases}$ is continuous is (are)

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