Partial differential function

[goatchurchprime]

If this function is smooth and differentiable, then a partial differential in each of the three axes would be a useful feature.

I've seen this simplex noise function used for generate blobby surfaces by plotting the set of points where f(x,y,z)=0. Knowing the differential at that each point would mean we would know the normal of the surface without needing to sample the function six times. It could also be useful for benchmarking various scipy.optimize.minimize() which require this differential function.

This challenge is for a mathematician with too much spare time on their hands.

[lmas]

I'm no mathematician so this is way over my head and my simple port. If I get a free weekend sometime I might give this a look, but will gladly accept any help and pull requests :)