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单词 Reciprocal rule
释义

Reciprocal rule

中文百科

倒数定则

倒数定则是数学中关于函数的倒数的导数的一个计算定则。

设有函数g(x)，则其倒数\frac{1}{g(x)}的导数为

\frac{d}{dx}\left(\frac{1}{g(x)}\right) = \frac{- g'(x)}{(g(x))^2}
\frac{1}{x^2 + 2x}的导数为：
\frac{d}{dx}\left(\frac{1}{x^2 + 2x}\right) = \frac{-2x - 2}{(x^2 + 2x)^2}.
\frac{1}{\cos(x)}的导数为：
\frac{d}{dx} \left(\frac{1}{\cos(x) }\right) = \frac{\sin(x)}{\cos^2(x)} = \frac{1}{\cos(x)} \frac{\sin(x)}{\cos(x)} = \sec(x)\tan(x).
英语百科

Reciprocal rule 倒数定则

In calculus, the reciprocal rule is a shorthand method of finding the derivative of a function that is the reciprocal of a differentiable function, without using the quotient rule or chain rule.

The reciprocal rule states that the derivative of 1/g(x) is given by
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更新时间：2025/6/20 0:16:39