If x=6t,y=4t^3, then the value of (d^2y)/(dx^2) is :

The correct answer is Option (4) → $\frac{2}{3}t$

$x=6t$,         $\frac{dx}{dt}=6$

$y=4t^3$,     $\frac{dy}{dt}=12t^2$

$⇒\frac{dy}{dx}=\frac{12t^2}{6}=2t^2$

$⇒\frac{d^2y}{dx^2}=4t×\frac{dt}{dx}=4t×\frac{1}{6}$

$=\frac{2}{3}t$