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,