If $x=5t $ and $y=\frac{5}{t}$, then $\frac{d^2y}{dx^2}$ at $t=1$ is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{2}{5}$
$x=5t$
$\frac{dx}{dt}=5$
$y=\frac{5}{t}$
$\frac{dy}{dt}=-\frac{5}{t^2}$
$⇒\frac{dy}{dx}=-\frac{1}{t^2}$
$⇒\frac{d^2y}{dx^2}=\frac{2}{5t^3}$
$⇒\left.\frac{d^2y}{dx^2}\right|_{t=1}=\frac{2}{5}$