Finite Difference Differentiation (scipy.differentiate)

SciPy differentiate provides functions for performing finite difference numerical differentiation of black-box functions.

derivative(f, x, *[, args, tolerances, ...])	Evaluate the derivative of a elementwise, real scalar function numerically.
jacobian(f, x, *[, tolerances, maxiter, ...])	Evaluate the Jacobian of a function numerically.
hessian(f, x, *[, tolerances, maxiter, ...])	Evaluate the Hessian of a function numerically.