This is strange. @Torsten gave you a simple solution. Your response was that the excercise is so simple, that it should be doable using direct computations. In fact, it is quite simple. So do it.
In fact, you know how to form a matrix, since you wrote that part in your question. So just compute the derivatives. Where is the problem? Do you not know how to use diff? Are you not allowed to use diff? If you can use diff, then do so. If not, then you must understand what the definition of a derivative is, as a limit, and surely you have learned how to approximate a derivative? So what are you not saying? Don't just say it is easy, as you would not be asking the question if it was really that easy for you.
IF the entire thing is too complex for you to do, then take one piece at a time. You have a function (actually, two of them), of two variables. Differentiate each piece with respect to each variable, using whatever means you wish. Then do that 4 times, and put it together.
