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

$\frac{1}{2 a t^3}$ $\frac{1}{a t^3}$ $\frac{-1}{2 a t^3}$ $-\frac{1}{t^2}$

$\frac{-1}{2 a t^3}$

The correct answer is Option (3) - $\frac{-1}{2 a t^3}$