The graph of a function $f: R \to R$ is shown below, where $R$ is a real numbers

Then which of following statements is correct?

If $e^y(x+1) = 1$, then $\dfrac{d^2y}{dx^2}$ is equal to

If $\sqrt{1-x^2} + \sqrt{1-y^2} = a(x-y)$, then $\frac{dy}{dx} =$

If $e^y(x+1)=1$, then

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

If the function $f(x)=\begin{cases}3x-6, & x \le 5 \\ 4k, & x>5\end{cases}$ is continuous at $x=5$, then the value of $k$ is:

If $y = \frac{\sqrt{x+1} + \sqrt{x-1}}{\sqrt{x+1} - \sqrt{x-1}}$, then $(x^2-1)^{3/2} \frac{d^2y}{dx^2} =$