# How do you find the second derivative of xy =32?

$\frac{64}{x} ^ 3$
$y = \frac{32}{x}$ so
$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{32}{x} ^ 2$ and
$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = \frac{d}{\mathrm{dx}} \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = \frac{64}{x} ^ 3$