Throughout my time doing research in multimodal machine learning, I happened accross many times where I had to find the higher order derivative of a matrix function. The straightforward way to find these is to use the kronecker delta. But unfortunately this results in some high order tensors as the derivatives. In an attempt to understand these higher order tensors better, I developed a neat way to express them in another format, which makes more intuitive sense to me. You can find it here (link to pdf).