continuous-time system so if we actually evaluate the gradients DX DT is negative Y and dy DT is positive x the sign difference is because one of them is trying to minimize the value of function and one of them is trying to maximize it if we then go ahead and solve this differential equation to find the directions I guess there's a lot of different ways of doing it depending on exactly which pattern matching technique you're most comfortable with my particular approach is to differentiate the second equation with respect to T