I see that I can declare a function with (say)
public double Function(double parameter)
but what if I do want to take the derivative of tha
If you're thinking of symbolic manipulation of formulae then you're better off doing your derivations in languages like Maple or Mathematica. They're designed for symbolic computation.
EDIT: If Maple and Mathematica are too expensive for you then there are other options. Wikipedia has a fairly complete listing of computer algebra packages. http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems