numerical differentiation with constraints on the parameter space

I want to compute the derivatives of a non-analytic function. I see there are packages available (for example, DERIVESTsuite) to compute the numerical derivatives but they do not have any option to put constraints on the parameter space. Please suggest some ways to compute the numerical derivatives with constraints on the parameter. I have only one constraint: the parameters can take only positive values.

For example, suppose I have a function f(x) which is defined as a MATLAB function,

where x=[x1,x2] is a vector with x1>0 and x2>0

and I want to compute Jacobian of f(x) w.r.t. x.

The problem is that the function f(x) cannot be computed for negative values of either x1 or x2. So, if my program tries to compute the partial derivative of f(x) w.r.t. x1 at x1=0 using the formula

(f(1)-f(-1))/2,

it will give an error.

[Ameer Hamza]

Can you give an example? What type of constraint are you applying to differentiation?

[Abhinav]

I have now included an example in the question. Let me know if the question is clearer now.

[Ameer Hamza]

How if f(x) defined? You mentioned "non-analytic function". Is it defined as a MATLAB function?

[Abhinav]

Yes, it is defined as a MATLAB function.