In advanced mathematics, are derivatives and limits the same? Are the left and right derivatives and the left and right limits the same? Please explain in detail the differences and similarities betwe

In advanced mathematics, are derivatives and limits the same? Are the left and right derivatives and the left and right limits the same? Please explain in detail the differences and similarities between the two.

The derivative is a limit in a special format (that is, the ratio of the dependent variable of the function y=f(x) to the variable of the independent variable when the independent variable tends to 0) , and the general limit is not a derivative;

The left and right derivatives are the limits of the above format when the independent variable tends to 0 from one side. Similarly, the general left and right limits are not left and right derivatives.

< p> In short, the derivative is the limit, and the limit is not necessarily the derivative.