Looking for an easy way to find partial derivatives of an implicit equation. For example:
Find $\partial z/\partial x$ and $\partial z/\partial y$ if $z$ is defined implicitly as a function of $x$ and $y$ by the equation $$x^3+y^3+z^3+6xyz=1$$
Clear[x, y, z]; eqn = x^3 + y^3 + z[x, y]^3 + 6 x y z[x, y] == 1; Solve[D[eqn, y], D[z[x, y], y]] /. z[x, y] -> z
But I still like what I see on this page better.