The basic elementary function is a kind of function which is a real or complex exponential function, logarithmic function, power function, trigonometric function and inverse trigonometric function after finite four operations and finite synthesis.

Elementary function, only in the definition domain and the definition interval must be continuous. Didn't say it would conduct electricity.

For example, the cubic of f(x)= x follows this elementary function and is continuous at x=0, but it is not differentiable.

Elementary function is a function obtained by finite four operations and compound operations of basic elementary function.

Advanced mathematics divides basic elementary functions into five categories: power function, exponential function, logarithmic function, trigonometric function and inverse trigonometric function.

Mathematical analysis divides basic elementary functions into six categories: power function, exponential function, logarithmic function, trigonometric function, inverse trigonometric function and constant function.