一元函数微分学_4-57（Differential calculus of unary functions _4-57）.docVIP

一元函数微分学_4-57（Differential calculus of unary functions _4-57） Documents from the network, I collected, finishing, and if there are omissions, errors, but also please correct me! The second chapter unary function differential calculus Section 2.1 derivative and differential I. main contents The concept of a derivative 1. derivative: defined in a neighborhood, 2. left derivative: Right derivative: Theorem: continuous on the left (or right) neighborhood It can be guided and limited; Then: (or:) 3., the necessary condition of differentiable function: Theorem: at the point of continuity 4. necessary and sufficient conditions for differentiable functions: Theorem: existence, And exist 5. derivative function: It can be guided everywhere Y Geometric properties of 6. derivatives: Its the point on the curve The slope of the tangent O x0 x Two law of derivation 1. basic derivation formula: Four operations of 2. derivatives: 1O 2O 3O 3. derivatives of composite functions: Or, To pay attention to and the difference: Represents the derivation of an argument by a composite function; Represents a composite function for derivation of an intermediate variable 4. higher order derivatives: The derivative of the n order of a function is equal to the derivative of its n-1 derivative The concept of three differential 1. differential: defined in a neighborhood, Of which: nothing to do with, is relatively high An infinitesimal quantity of a step: It is said that the place is differentiable and recorded: 2. equivalent relation between derivative and differential: Theorem: differentiable at the point, derivable at the point, And: 3. differential form invariance: Whether u is an independent variable or an intermediate variable, function Differentiation has the same form Example analysis Case 1. is set, and, Equals A.1 B.0 C.2 D.. [...] Solution: * (C. D) Example 2. is set where the place is continuous Solution: Misunderstand: L The result is the same, but the procedure is wrong Because the know