If $x=5t^3$ and $y=3t^4,$ then $\frac{d^2y}{dx^2}$ is equal to :

$\frac{4}{75t^2}$

The correct answer is Option (2) → $\frac{4}{75t^2}$

$x=5t^3$ and $y=3t^4$

$\frac{dx}{dt}=15t^2$, $\frac{dy}{dt}=12t^3$

$⇒\frac{dy}{dx}=\frac{12t^3}{15t^2}=\frac{4}{5}t$

$⇒\frac{d^2y}{dx^2}=\frac{4}{5}×\frac{dt}{dx}=\frac{4}{5}×\frac{1}{15t^2}=\frac{4}{75t^2}$