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单词 Differentiable function
释义

Differentiable function

英语例句库

The uniqueness theorem of generalized quasi-analyticity of the infinitely differentiable functions in some closed angular domain is extehded to the functions of several complex variables.

摘要把无穷可微函数类在角形闭区域上的唯一性结果推广到了多维情形。

中文百科

可微函数

一个可微函数的图像
魏尔斯特拉斯函数连续，但在任一点都不可微
Schwarz: Graph der Funktion fRot: Graph der linearen Funktion g, die f in der Nähe der Stelle x0 approximiert
Zur 2. Definition der Differenzierbarkeit

在微积分学中，可微函数是指那些在定义域中所有点都存在导数的函数。可微函数的图像在定义域内的每一点上必存在非垂直切线。因此，可微函数的图像是相对光滑的，没有间断点、尖点或任何有垂直切线的点。

一般来说，若X0是函数ƒ定义域上的一点，且ƒ′(X0)有定义，则称ƒ在X0点可微。这就是说ƒ的图像在(X0, ƒ(X0))点有非垂直切线，且该点不是间断点、尖点。

英语百科

Differentiable function 可微函数

A differentiable function
The absolute value function is continuous (i.e. it has no gaps). It is differentiable everywhere except at the point x = 0, where it makes a sharp turn as it crosses the y-axis.
An ordinary cusp on the cubic curve (semicubical parabola) x3 – y2 = 0, which is equivalent to the multivalued function f(x) = ± x3/2. This relation is continuous, but is not differentiable at the cusp.
Differentiable functions can be locally approximated by linear functions.

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain. As a result, the graph of a differentiable function must have a (non-vertical) tangent line at each point in its domain, be relatively smooth, and cannot contain any breaks, bends, or cusps.
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更新时间：2025/6/19 10:21:23