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

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

$x=at^2,y=2at$

so $\frac{dx}{dt}=2at$ ...(1)

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

so $\frac{d^2y}{dx^2}=-\frac{1}{t^2}\frac{dt}{dx}$ from (1)

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