I will put this work on the self now. There are four ways with respect to computing partial derivatives, determined by "partialDersInputChoice":

1: none

2: partial derivatives of d wrt p,h,X
In two-phase region: numerical differentiation for all derivatives
In single phase region: dddX is numerical and others are analytical

3: partial derivatives of d wrt p,h,X
In two-phase region: pseudo analytical (similar procedure as pure fluid - they give almost same result but with less CPU effort)
In single phase region: dddX is numerical and others are analytical

4: partial derivatives of d and h wrt p,T,X
In two-phase region: numerical differentiation for all derivatives
In single phase region: dddX is numerical and others are analytical

The fourth method is the only one that compares exactly with stepping forward in u,d,X (the baseline with most CPU effort) It is quicker in two-phase region compared to method 2, because T and P are equilibrium quantities..

Note that the dddX derivative is the difference in dddX1|X2=const-dddX2|X1=const