#### Derivatives

Definition

The geometric meaning reflects the function y = f (x) along the positive direction of X axis at a certain point**Rate of change**。

The rate of change of the physical meaning representation function at this point (instantaneous)

#### partial derivative

Multiple independent variables are involved. For two independent variables*Z=f(x,y)*Is a 3D space. The derivative is a plane, and there is only one tangent of the point on the curve. There are countless for surfaces.

The partial derivative of a multivariable function is its derivative with respect to one of the variables, while keeping the other variables constant.

The geometric meaning reflects the rate of change of function z = f (x, y) along the positive direction of coordinate axis in a plane with constant variables

The physical meaning of partial derivative**Rate of change in the positive direction of the axis**

#### Directional derivative

Definition: the directional derivative of a scalar field at a point along a vector direction, which describes the instantaneous rate of change of the scalar field near the point along the vector direction

The physical meaning of directional derivative indicates that the function follows a certain point**Rate of change in a particular direction**

#### gradient

Meaning of gradient: at a certain point in variable space, which direction does the function have the maximum change rate.

The magnitude of the gradient is the directional derivative