If $x=4 t^2, y=8 t$, then $\frac{d^2 y}{d x^2}$ is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $-\frac{1}{8 t^3}$
$x=4 t^2, y=8 t$
$\frac{dx}{dt}=8t$
$\frac{dy}{dt}=8$
$⇒\frac{dy}{dx}=\frac{1}{t}⇒\frac{d^2y}{dx^2}=-\frac{1}{t}\frac{dt}{dx}=-\frac{1}{8 t^3}$
$\frac{d^2y}{dx^2}=-\frac{1}{8 t^3}$