The relationship between these properties of multivariate functions is that differentiability is the strongest property, that is, differentiability will inevitably lead to the existence of partial derivatives and continuity. On the contrary, the existence and continuity of partial derivatives cannot be deduced from each other (there is no direct relationship), that is, the partial derivatives of continuous multivariate functions cannot exist; Partial derivatives all have multivariate functions or can be discontinuous. Partial derivative is more differentiable than function, which is a necessary and sufficient condition for differentiability. Relevant examples can be found in mathematical analysis books.