Eye of depth (18) -- partial derivative

One 、 Partial derivative

Partial derivative of a variable , Then the other variables are regarded as constants

It can be directly regarded as established , Don't stick to conditions

Two 、 Derivation rule of multivariate composite function , Chain derivation rule

Here is a good technique , You can see z To t There are several paths

The method of finding partial derivatives for multivariate time
For example, yes. x Finding partial derivatives , Just see x The path of , There are a few , After what

The key is to draw a quasi chain relationship

3、 ... and 、 Directional derivatives and gradients and their applications

give an example

Positive direction of gradient , It is the direction with the fastest gradient growth .
The negative direction of the gradient , It is the direction in which the gradient decreases fastest

Four 、 Taylor formula of multivariate function and Hessen torch matrix

Generally, second order

Hessian matrix is a symmetric matrix

5、 ... and 、 Extreme value of multivariate angle

6、 ... and 、 Derivation of distance matrix

7、 ... and 、 The application of matrix derivation in deep learning