Hello, I'm trying to solve a non linear equation using a computer program. It's a discrete equation and I'm not really sure how to get the Jacobian. This is the equation and how I've approached it

Eqn:

I want to solve this equation for

So, for example:

I let , and (Denominator)

This leaves me with:

At this stage my equation is a function

I differentiate the function next

Differentation with respect to gives me:

(1)

Differentation with respect to gives me:

The program I'm using to solve this equation needs the Jacobian. I know the Jacobian is

The problem is I have no idea how to apply this to the two equations I obtained.

If anyone can help me with this I would be very grateful.