[ncray]

Yeah, tabako's right. Maybe to be a little bit more clear,
d^2e / (dp_i*dp_j) = d/dp_i * de/dp_j = d/dp_i * h*_j = dh*_j / dp_i
And since d^2e / (dp_i*dp_j) = d^2e / (dp_j*dp_i) = d/dp_j * de/dp_i = d/dp_j * h*_i = dh*_i / dp_j

We have that dh*_j / dp_i = dh*_i / dp_j