Here is a first derivative term
[Graphics:../Images/dimensionless_gr_15.gif]

Here is a convenient input format for Mathematica

[Graphics:../Images/dimensionless_gr_16.gif]
[Graphics:../Images/dimensionless_gr_17.gif]

Now we do the substitutions for the derivatives as described above.  

[Graphics:../Images/dimensionless_gr_18.gif]
[Graphics:../Images/dimensionless_gr_19.gif]
[Graphics:../Images/dimensionless_gr_22.gif]


Converted by Mathematica      November 6, 2000