Using the chain rule,
Differentiating (a time shifted version of) the eqn.1.2 wrt 
Finally we get the required probability, by substituting for 
in eqn.1.22 (keeping
in mind that 
in this case), which is obtained
by substituting eqns.1.28 and 1.24 in eqn.1.27.
Usually this is given the following form, by first substituting for
from eqn.1.21 and then substituting from
eqn.1.14.
If the continuous densities are used then 
can be
found by further propagating the derivative 
using the chain rule.
The same method can
be used to propagate the derivative (if necessary) to a front end
processor of the HMM. This will be discussed in detail later.
