If $x=at^2$ and $y=2at$, then $\frac{d^2 y}{d x^2}$ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) - $\frac{-1}{2 a t^3}$
$\frac{dx}{dt}=2at$, $\frac{dy}{dt}=2a$
$\frac{dy}{dx}=\frac{1}{t}$ so $\frac{d^2t}{dx^2}=\frac{-1}{t^2}\frac{dt}{dx}$
$=\frac{-1}{2 a t^3}$