Estimate derivatives by simply passing in a complex number to your function. A single (complex) function evaluations computes both the function's value (Re) and the derivative (Im). Is it always possible to do this? I mean with a standard code form industry (Nastran, Fluent etc...)?
Comparison of Symbolic/Finite Differences/DIRECT/ADJOINT Method on a really simple mechanical system (2DOFs).
Play with the code for checking Symbolic with Finite Differences. Play with
BTW, How Nastran is doing for gradient computation on SOL2OO ? gradient nastran