First of all, the function refers to data set A, and through some mapping relationship, data set B can be obtained, for example, y=2x. Generally speaking, one dollar can buy two pomegranates; Then you can buy four pomegranates for two dollars ... this correspondence constitutes a function.

Secondly, differentiability means that the function is continuous within a certain range. The concept of derivative is geometrically slope. For example, y = x 2, and its derivative form is y'=2x.

Finally, differentiability means that the function must be continuous in this range, but continuous does not mean that the function is differentiable in the corresponding range.