How to derivative Navier-Stokes by control vector
 

I'm reading one research paper[1],I got lots of trouble,because I dont have CFD background,I really need your guys help.My question is if u is consisted by serveal of control parameters,how to derivative Navier-Stokes by control vector u?

df/du=? dv/du=?

http://grail.cs.washington.edu/proje...okeControl.pdf

Thanks!