If $x=at^2 $ and $y = a^3t^3 ,$ then $\frac{d^2y}{dx^2}$ will be :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{3a}{4t}$
$\frac{dx}{dt}=2at$
$\frac{dy}{dt} = 3a^3t^2$
$\frac{dy}{dx}=\frac{3a^3t^2}{2at}=\frac{3a^2t}{2}$
$\frac{d^2y}{dx^2}=\frac{3a^2}{t}\frac{dt}{dx}=\frac{3a^2}{2×2at}=\frac{3a}{4t}$