R help - Mar 2010 - partial differentiation of a dynamic expression

Hello,
 
It is possible to use 'deriv' when the expression itself is dynamic? I
have data where the conditional mean is time-varying (like a GARCH(1,1) model)
as
 
mu_{t} = omega1 + alpha1*N_{t-1} + beta1*mu_{t-1}.
 
The parameter vector is c("omega1", "alpha1",
"beta1") and N_t is the observation at each time.
 
I want two things:
1. the derivative of mu_t with respect to each parameter. So for example, the
first derivative with respect to omega1 is "1 + beta1* d mu_{t-1}/ d
omega1."
2. Once I have the expression in 1, I want its first partial derivative.
 
Ultimately, I want to find the root of an estimating function using
Newton-Raphson, where
 
param <- param - solve(mat)%*% param, 
 
and where param is an estimating function which has first partial derivatives in
it and 'mat' is a matrix which involves the first partial derivatives of
elements in 'param'.
 
Thanks,
Melody
 
 

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