Найти полный дифференциал функции заданной уравнением z^3-3*x*y*z=a^3

Решите задачу:

$z^3-3xyz=a^3\; ,\; \; a=const\\\\F(x,y,z)=z^3-3xyz-a^3\\\\\frac{\partial z}{\partial x}=-\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial z}}=-\frac{-3yz}{3z^2-3xy}=\frac{yz}{z^2-xy}\\\\\frac{\partial z}{\partial y}=-\frac{\frac{\partial F}{\partial y}}{\frac{\partial F}{\partial z}}=-\frac{-3xz}{3z^2-3xz}=\frac{yz}{z^2-xz}\\\\dz= \frac{yz\, dx}{z^2-xy} + \frac{xz\, dy}{z^2-xz}$