The concept of multiple functions, such as continuity, differentiable, partial derivative, directional derivative, is abstract and complex. They are the four special difficulties in teaching. In order to comprehend the connotation and concept of them, through concrete examples, we make full use of the concepts and theorems, and discuss in detail the causal connection between the conditions and conclusions of each concept, and the inner link between these basic concepts, which reduce the difficulty of teaching higher mathematics, which help beginners accept these knowledge easily.