Unfortunately the Nabla operator is of no help here. It can only be used for scalar valued functions like

but it fails here as the function given by @hegel returns a 2x2 matrix:

It is a great pity and a major shortcoming that Prime is generally not very good at dealing with vector functions and thus the partial derivative according to a vector component is not possible.
A clumsy workaround could be this (assuming that the input function f() is for good reason defined as a vector function and not as a function with three separate arguments and also assuming that the partial derivatives should be assigned to vector functions as well):

Prime 9 worksheet attached