1
the derivative of sth
The derivative of the function is calculated using basic rules.
这个函数的导数是通过基本规则计算出来的。
引出之物；派生物；衍生字
先理解核心含义，再看它在真实句子里的用法。
引出之物；派生物；衍生字
the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
The derivative of the function is calculated using basic rules.
这个函数的导数是通过基本规则计算出来的。
数学微分的结果；一个量相对于另一个量的瞬时变化；df(x)/dx
the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
从另一化合物获得或视为来源于另一化合物的化合物
a compound obtained from, or regarded as derived from, another compound
其价值基于另一证券的金融工具
a financial instrument whose value is based on another security
In calculus, we learned that the derivative of x squared is 2x.
在微积分中，我们学到了 x 平方的导数是 2x。
To find the speed of the car at that exact moment, you need to calculate the derivative.
要计算汽车在那一瞬间的速度，你需要计算导数。
The students practiced how to find the derivatives of various simple functions.
学生们练习了如何求各种简单函数的导数。
The derivative of the function is calculated using basic rules.
这个函数的导数是通过基本规则计算出来的。
Students need to find the derivative of the equation.
学生们需要求出这个方程的导数。
Not this
This new product is a derivative from the original design.
Use this
This new product is a derivative of the original design.
表示“某物的衍生物”时，derivative 作为名词后接介词 of 而非 from，这是固定搭配用法。
Not this
These derivatives are very important in modern finance.
Use this
This derivative is very important in modern finance.
此处指“一个具体的衍生金融产品”，应使用单数形式 derivative，而非复数 derivatives，避免不必要的复数误用。
Focus on the distinctions below. Other candidates are kept compact until a reliable usage note is available.
函数的导函数
The derivative of a function represents its instantaneous rate of change.
函数的导函数表示其瞬时变化率。
计算导数
Students need to calculate the derivative of the given equation.
学生需要计算所给方程的导数。
一阶导数
The first derivative indicates whether the function is increasing or decreasing.
一阶导数表示函数是递增还是递减。
偏导数
In multivariable calculus, we often compute the partial derivative with respect to one variable.
在多变量微积分中，我们经常计算对某一个变量的偏导数。
二阶导数
The second derivative tells us about the concavity of the graph.
二阶导数告诉我们图像的凹凸性。
Use derivative naturally, then get feedback on meaning, tone, grammar, and phrasing.
Revisit a common error or keep this word in your review list.
语域：formal 常见场景：mathematics、calculus 此义项多用于数学和科学领域，属于正式用语。
arrive, deprive, derive, survive 的拼写结尾均为 -ive，但只有 deprive 和 derive 的重读音节元音及后续发音 /aɪv/ 与 derivative 的 /vʌtɪv/ 不同，不构成押韵。拼写相似的 captive, native 等词发音不同，不列入。
Collins 词频等级为 1，建议结合例句记忆，而不是只背中文释义。
页面下方列出了常见词形变化。学习时注意它们在句子中的语法位置。
Dictionary facts from ECDICT.