Answer
$\dfrac{d^2y}{dx^2}=-\dfrac{36}{y^3}.$
Work Step by Step
$\dfrac{d}{dx}(x^2)-\dfrac{d}{dx}(y^2)=\dfrac{d}{dx}(36)\rightarrow$
$2x-\dfrac{dy}{dx}(2y)=0\rightarrow\dfrac{dy}{dx}=\dfrac{x}{y}.$
Second Derivative:
$\dfrac{d}{dx}(\dfrac{dy}{dx})=\dfrac{d}{dx}(\dfrac{x}{y})\rightarrow$
$\dfrac{d^2y}{dx^2}=\dfrac{y-\dfrac{dy}{dx}(x)}{y^2}=\dfrac{y^2-x^2}{y^3}=-\dfrac{36}{y^3}.$
