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In what range can mathematical functions be derived? What do you mean? Are there any examples?
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.