Using the chain rule for any of the likelihoods, free or clamped,
Differentiating eqns.1.39 and 1.40 wrt
, to get two results for free and clamped cases and
using the common result in eqn.1.25, we get substitutions for
both terms on the right hand side of eqn. 1.41. This substitution
yields two separate results for free and clamped cases.
where is a Kronecker delta.
Substitution of eqns. 1.42 and 1.43 in the
eqn.1.38(keeping in mind that in this
case) gives the required result,