If x=at^2 and y=2at, then (d^2y)/(dx^2)=

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

$x=at^2$ and $y=2at$

$\frac{dx}{dt}=2at$, $\frac{dy}{dt}=2a⇒\frac{dy}{dx}=\frac{1}{t}$

$\frac{d^2y}{dx^2}=-\frac{1}{t^2}×\frac{dt}{dx}$

$=-\frac{1}{2at^3}$