If $x=6t^2, y = \frac{6}{t^2}, $ then $\frac{d^2y}{dx^2}$ is equal to :

$\frac{1}{3\, t^6}$

The correct answer is Option (2) → $\frac{1}{3\, t^6}$

$\frac{dy}{dt}=\frac{-12}{t^3},\frac{dx}{dt}=12t$

$∴\frac{dy}{dx}=\frac{-12}{t^3×12t}=\frac{-1}{t^4}$

$⇒\frac{d^2y}{dx^2}=\frac{t^4}{t^5}×\frac{1}{12t}$   $[\frac{dt}{dx}=\frac{1}{12t}]$

$=\frac{1}{3t^6}$