Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版:英文原文完整保留,中文紧随对应单元;术语采用 v20260916 确认表,自动语义审校结果可追溯。

Properties of the Derivative

导数的性质

The derivative has certain special properties when applied to combinations of functions.

当导数应用于函数组合时,具有某些特殊性质。

Derivative of the product of two functions

两个函数乘积的导数

If the function f(x) is a product of two functions m(x) and n(x), then the derivative of this product is

如果函数 f(x) 是两个函数 m(x) 和 n(x) 的乘积,那么这个乘积的导数为

Derivative of the sum of two functions

两个函数之和的导数

If the function f(x) is a sum of two functions m(x) and n(x), then the derivative of this sum is simply the sum of the derivatives:

如果函数 f(x) 是两个函数 m(x) 和 n(x) 的和,那么这个和的导数就是这两个导数的和:

Chain rule for differentiation

微分的链式法则

If the function y = f(x) and x=g(z), then the derivative of y with respect to z can be written as a product of derivatives:

如果函数 y = f(x) 且 x = g(z),则 y 对 z 的导数可以表示为两个导数的乘积:
Index

Derivative concepts
索引导数概念
 
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