For the curve $xy= 6,$ the value of $\frac{d^2y}{dx^2}$ at y = 3 is :

$\frac{3}{2}$

The correct answer is Option (1) → $\frac{3}{2}$

$xy= 6$ at $y=3,x=2$

so differentiating wrt x

$y+x\frac{dy}{dx}=0$

at $y=3,x=2$

$\frac{dy}{dx}=-\frac{3}{2}$

differentiating again wrt x

$\frac{dy}{dx}+\frac{dy}{dx}+x\frac{d^2y}{dx^2}=0$

so $\frac{d^2y}{dx^2}=\frac{3}{2}$