Derivation is a calculation method in mathematical calculation, which is defined as the limit of the quotient between the increment of dependent variable and the increment of independent variable when the increment of independent variable tends to zero.

When a function has a derivative, it is said to be derivative or differentiable. The differentiable function must be continuous. Discontinuous functions must be non-differentiable.

Extended data:

The first derivative represents the rate of change of the function, and the most intuitive performance lies in the monotonicity of the function. Theorem: Let f(x) be continuous in [a, b] and have the first derivative in (a, b), then:

(1) If in (a, b), f' (x) >; The graph of 0, f(x) on [a, b] increases monotonously;

(2) If f'(x) in (a, b)

(3) If f'(x)=0 in (a, b), the graph of f(x) on [a, b] is a straight line parallel to (or coincident with) the X axis, that is, it is constant on [a, b].

The derivative of a function is the slope of the tangent at a point. When the function monotonically increases, the slope is positive, and when the function monotonically decreases, the slope is negative.

Derivative and differential: differential is also a linear way to describe the change of a function around a point. Differential and derivative are two different concepts. However, differentiability and differentiability are completely equivalent for univariate functions.

A differentiable function whose differential is equal to the derivative multiplied by the differential dx of the independent variable, in other words, the quotient of the differential of the function and the differential of the independent variable is equal to the derivative of the function. Therefore, the derivative is also called WeChat business. The differential of the function y=f(x) can also be written as dy=f'(x)dx.

References:

Baidu encyclopedia-derivative