The curvature equation for implicit functions, level sets is usually given in two forms: one is the divergence of the gradient of the unit normal:
$\kappa = \bigtriangledown \cdot \frac{\bigtriangledown \phi}{|\bigtriangledown \phi|}$
and the other is
$\kappa = \frac{\phi_{xx}\phi_y^2 - 2\phi_x\phi_y\phi_{xy} + \phi_{yy}\phi_x^2}{(\phi_x^2+\phi_y^2)^{3/2}}$
How do we derive the second equation from the first?