Is there a way to take the derivative of a function with a matrix as list of arguments.

Hopefully someone can point me in the correct direction. I am wondering if there is a way to take the derivative of a function where the list of arguments are passed to the function as a matrix. I have looked throughout the discussions and have not be able to locate a similar discussion (most deal with each function having a list of arguments). I have enclosed a simplified worksheet (only three variables). I do have a work around which I have included but the problem is that others usually have difficulty following the equations.