the discriminators input space might never be sampled there it's training process and then those particular inputs would not really have a defined behavior because they're just never trained but if you make those relatively weak assumptions we can then just solve for the functional derivatives where we regard D of X as being almost like this infinite dimensional vector where every x value index is a different member of the vector and we're just solving for a big vector like we're used to doing with calculus so in this case we take the