If x=5 t^3,y =7 t^4 , then (d^2y)/(dx^2) is equal to :

The correct answer is Option (4) → $\frac{28}{225\, t^2 }$

$x=5t^3,y=7t^4$

$\frac{dx}{dt}=15t^2$,  $\frac{dy}{dt}=28t^3$

$\frac{dy}{dx}=\frac{28t^3}{15t^2}=\frac{28t}{15}$

$\frac{d^2y}{dx^2}=\frac{28}{15}×\frac{dt}{dx}=\frac{28}{225\, t^2}$