The FortranCalculus (FC) compiler calculates partial derivatives on the fly. All a user does is enter their math equations & an objective (function) and FC finds the optimal solution for the given problem. The FC compiler is free (download and use) at least for the next year or two; see
http://fortranCalculus.info/apps/fc-compiler.html .
FC can solve Algebraic thru Differential equations while 'tweaking' parameters. FC uses Automatic Differentiation (AD) to calculate either the jocabian or Hessian matrix on the fly. Thus it is easy to use (next thing to a slide rule!) and exact. Most problems require a math model (i.e. your equations) and just a handful of other misc. code. Try it, you'll like it.
Our textbook,
http://fortranCalculus.info/textbook, has many (40+) FC example problem from industry. See and run other examples in fc-compiler's demo section. These demos examples can easily be modified to create one's own problem ... an hour or two and you should have solved your problem. :)
Please share FC with your colleagues, students, and friends. Knowing FC will help future students get jobs in industries that include math modeling.