Answer
$\frac{d^2y}{dx^2}=\frac{12xy^2-9x^4}{4y^3}$
Work Step by Step
$y^2=x^3$
$\frac{d}{dx}[y^2]=\frac{d}{dx}[x^3]$
$2y\frac{dy}{dx}=3x^2$
$\frac{dy}{dx}=\frac{3x^2}{2y}$
$\frac{d^2y}{dx^2}=\frac{d}{dx}[\frac{dy}{dx}]$
$\frac{d^2y}{dx^2}=\frac{d}{dx}[\frac{3x^2}{2y}]$
$\frac{d^2y}{dx^2}=\frac{6x2y-3x^22\frac{dy}{dx}}{(2y)^2}$
$\frac{d^2y}{dx^2}=\frac{12xy-6x^2\frac{dy}{dx}}{4y^2}$
$\frac{d^2y}{dx^2}=\frac{12xy-6x^2\frac{3x^2}{2y}}{4y^2}$
$\frac{d^2y}{dx^2}=\frac{12xy-\frac{18x^4}{2y}}{4y^2}$
$\frac{d^2y}{dx^2}=\frac{12xy-\frac{18x^4}{2y}}{4y^2} \times \frac{2y}{2y}$
$\frac{d^2y}{dx^2}=\frac{24xy^2-18x^4}{8y^3}$
$\frac{d^2y}{dx^2}=\frac{12xy^2-9x^4}{4y^3}$
