Advanced numbers | [calculus of multivariate function] chain derivation method, implicit function derivation method, total differential form invariance, multivariate function extremum

 

One 、 Differentiation of multivariate functions

1、 chain rule

 

 

 

 

 

 

 

 

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 2、 Invariance of total differential form

  Four operational properties of total differential operation

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 3、 Implicit function differential method

3.1 The case of an equation

•   Classic example

 

 

 

Odd number of negative 1 Even positive 1

 3.2 The case of equations

 

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3、 ... and 、 Extreme value and maximum value of multivariate function

1、 Unconstrained extremum

 2、 Conditional extremum and Lagrange multiplier method

 3、 Max min

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Four 、 Frequently asked questions and classic examples

1、 continuity 、 Partial derivative 、 The concept of total differential and the relationship between them

Differentiable but discontinuous counterexamples

 

 

 

2. Partial derivative and total differential of composite function

 

  After derivation f1,f2, Still compound ！

 

3. Partial derivative and total differential of implicit function

 4. Find the extreme value ( Unconditional )

 

  Two ways to solve the original function ：① Partial integral   ② Make a difference

 5. Find continuous function f(x,y) In a bounded closed region D The maximum and minimum values on

 

 6. Maximum and minimum application questions .