Show that a unit normal to the surface $x^3y^3 + y - z + 2 = 0$ is given by $\bold{n} = \frac{1}{\sqrt{2}}(\bold{j} - \bold{k})$
In general, the surface given by $f(x,y,z)=0$ will have the vector $\nabla f(x_0,y_0,z_0)$ as normal at $f(x_0,y_0,z_0)$.