Number of party wizards and gradients

1. Basic Concepts

Party Wizard Number : is a number that reflects the rate of change of f (x, y) at the P0 point along the direction v.

partial derivative : is the number of multiple (one per element), refers to the multivariate function along the axis of the direction of the Party Wizard , so the two-ary function has two partial derivatives.

biased function : is a function, a function of the partial derivative of a point.

gradient : is a vector; each element is a partial derivative of a function against a unary variable; it has both a size (its size is the maximum number of wizards) and a direction.

2. Number of party guides

reflects the rate of change of f (x, y) at the P0 point along the direction v.

Examples are as follows:

2.0-Party wizard number calculation Formula

2.1 derivative

2.2 The geometrical meaning of the partial derivative of two Yuan function

2.3 Partial derivative function

the relationship between partial derivatives and partial derivative functions:

The partial derivative is the function value of the biased function at the specified point, so when the partial derivative is obtained, the biased derivative function can be obtained first, and then the point is placed into the partial derivative function to find the partial derivative of the function at this point.

3. Full differential

4. Gradients A gradient is a vector; it has both size and direction.

4.1 Geometrical Meanings

The gradient direction of the function z=f (x, y) at Point P0 is the maximum direction of the function change rate (the number of party wizards) .

The direction of the gradient is that the function f (x, Y) is in the fastest growing direction, and the gradient modulus is the maximum value of the directional derivative.

Number of party wizards and gradients