Broadly speaking, there are many cases in which functions are not derivable, but at present, the derivability of functions in higher mathematics research is mainly based on elementary functions, or piecewise functions, and composite functions composed of several elementary functions. On the basis of this research, the derivability is generally manifested in the following aspects:

It is easy to understand that the function is not continuous at some point.

(2) At a certain point, the left and right derivative values of the function are not equal, which is the so-called cusp. For example, y=∣x∣ is at x=0.

③ The derivative value of the function tends to infinity at a certain point, for example, y = x (1/3) when x=0.