Why Hessian should be doubled?

I found in the below tutorial on multi:softprob, hessian seems to be doubled compared to theoretical value.
(i.e. theoretical diagonal value of hessian should be p (1 - p), however, in this tutorial uses 2 * p (1 - p).)


Can we share some theoretical background about this?

(I derived h = p * (1 - p) from cross entropy objective function)