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B1 verb #7,000 most common 9 min read

推导

tuidao Top 7,000

Practice it Examples Notes & Tips 推导 in 30 Seconds

Explanation 推导 in your Level:

At the A1 level, '推导' (tuīdǎo) is a very advanced word that you likely won't need for daily survival. However, you can think of it as a super-powered version of 'thinking' (想 - xiǎng). Imagine you are in a math class. When the teacher shows you how 1+1=2 using a long explanation, they are '推导'-ing. At this level, just remember that '推' means 'push' and '导' means 'lead.' So, '推导' is 'pushing' your brain to 'lead' to an answer. You might see it in a very basic science textbook. Don't worry about using it yet; just recognize it as something smart people do when they solve hard problems. It's like 'calculating' but with more logic steps. Most A1 students should focus on '算' (suàn - to calculate) first, as it's much more common for simple math. '推导' is for when you become a scientist in Chinese!

By A2, you are starting to use more specific verbs. While you still use '想' (think) and '算' (calculate) most of the time, you might encounter '推导' in school-related contexts. If you are describing what you did in a math or science class, you could say '老师教我们推导公式' (The teacher taught us to derive formulas). This makes your Chinese sound more formal and academic. Remember that '推导' is a verb. You use it when you follow a path of logic to get to a result. It's different from '猜' (cāi - to guess) because '推导' requires reasons and steps. If you have a reason for every step you take to find an answer, you are '推导'-ing. It's a great word to use if you want to impress your teacher by showing you understand the *process* of learning, not just the final answer.

At the B1 level, you should be able to use '推导' (tuīdǎo) in specific contexts like math, logic, or formal discussions. You're moving beyond simple daily life into more complex topics. '推导' is a 'result-oriented' process. You usually '推导' *something* out (推导出来). For example, '根据这些数据，我们可以推导出未来的趋势' (Based on this data, we can derive future trends). Notice the use of '根据' (based on) – this is a very common partner for '推导.' You are also likely to see '推导过程' (derivation process) in textbooks. At this level, you should start distinguishing '推导' from '推理' (reasoning). '推理' is the general skill, like what Sherlock Holmes does. '推导' is the specific act of writing down the steps to prove a point or find a formula. It's a key word for anyone interested in business, science, or engineering in China.

At B2, you are expected to use '推导' (tuīdǎo) accurately in professional and academic settings. You should understand its nuance as a rigorous, logical derivation. It’s not just for math; it can be used for logical arguments in an essay. For instance, '作者通过严密的逻辑推导，证明了他的观点' (The author proved his point through rigorous logical derivation). Here, '严密' (rigorous) is a perfect adjective to pair with '推导.' You should also be comfortable using '推导' in the passive voice or as a noun. For example, '这个结论的推导并不容易' (The derivation of this conclusion was not easy). At this stage, you should also be aware of synonyms like '推断' (to infer) and '演算' (to calculate/operate). '推导' implies a more formal, step-by-step constructive process than '推断,' which can sometimes be a single leap of logic.

At the C1 level, '推导' (tuīdǎo) should be a natural part of your academic and professional vocabulary. You should be able to discuss the validity and methodology of a derivation. You might critique a '推导过程' for having logical loopholes (逻辑漏洞). You will encounter this word in high-level research papers, philosophical texts, and complex technical manuals. For example, '在量子力学中，波函数的推导是核心内容' (In quantum mechanics, the derivation of the wave function is a core element). You should also understand its metaphorical uses in social sciences, such as '推导' a social trend from historical patterns. At this level, you should be able to use the word with sophisticated adverbs like '递归地' (recursively), '公理化地' (axiomatically), or '演绎性地' (deductively). Your mastery of '推导' reflects your ability to engage with Chinese intellectual discourse at a deep level.

At the C2 level, '推导' (tuīdǎo) is a tool for precision in high-stakes intellectual environments. You understand the epistemological implications of the word—how '推导' functions as a bridge between axioms and theorems. You can use it to discuss the foundations of logic, such as the difference between inductive reasoning and '演绎推导' (deductive derivation). You might use it in a sentence like: '该理论的局限性在于其初始假设无法通过经验推导予以证实' (The limitation of the theory lies in the fact that its initial hypotheses cannot be verified through empirical derivation). You are also sensitive to the stylistic choice of using '推导' over more common words to convey a sense of scientific authority and formal rigor. Whether you are writing a doctoral thesis in Chinese or participating in a high-level policy debate, '推导' is the word you use to describe the structural integrity of your arguments and the mathematical certainty of your proofs.

Practice it Examples Notes & Tips

推导 in 30 Seconds

A formal verb meaning to derive or deduce using logic or mathematics.
Commonly used in academic and scientific contexts for formulas and laws.
Focuses on the step-by-step process of reaching a conclusion.
Often paired with '出' (chū) to indicate a successful derivation.

The Chinese verb 推导 (tuīdǎo) is a sophisticated term primarily used in academic, scientific, and logical contexts. At its core, it describes the mental or mathematical process of starting from known premises, axioms, or data and systematically working through logical steps to reach a new conclusion or formula. Unlike simple guessing, 推导 implies a rigorous, step-by-step progression where each stage is supported by evidence or established rules. In an English-speaking context, it most closely aligns with 'to derive,' 'to deduce,' or 'to infer' through formal logic.

Mathematical Context: In a math classroom, a teacher doesn't just give you a formula; they 推导 the formula on the blackboard to show you where it came from. This involves showing the algebraic steps that link a basic principle to a complex equation.
Logical Reasoning: In philosophy or law, one might 推导 a specific consequence from a general rule. It is the 'pushing' (推) of a thought along a 'path' or 'guide' (导) to its inevitable destination.

通过这个基本定律，我们可以推导出许多重要的结论。(Through this basic law, we can derive many important conclusions.)

The word is composed of two characters: 推 (tuī), meaning 'to push' or 'to infer,' and 导 (dǎo), meaning 'to lead' or 'to guide.' Together, they evoke the image of pushing a thought-train along the tracks of logic. You will hear this word most frequently in universities, research institutes, and high-level technical discussions. It is rarely used in casual daily conversation unless the speaker is being intentionally formal or discussing a complex problem-solving process. For instance, you wouldn't use 推导 to describe figuring out what to eat for dinner, but you would use it to describe how a detective 'derived' the identity of a killer from a series of clues.

Furthermore, 推导 carries a connotation of accuracy and necessity. If the logic is sound, the 推导 is considered valid. It is a foundational concept in the 'hard sciences' (STEM fields) in China. When students are asked to 'show their work,' they are essentially being asked to provide the 推导过程 (derivation process). This emphasis on the process reflects a deep cultural respect for methodology and rigorous intellectual labor. Understanding this word helps learners navigate formal Chinese academic literature and professional environments where logical rigor is paramount.

Using 推导 correctly requires understanding its role as a transitive verb, often followed by a result or a process. The most common structure is 推导 + 出 + [Conclusion/Formula]. The particle '出' (chū) indicates the successful completion of the derivation, resulting in something tangible or clear.

Pattern 1: Deriving a Formula: Subject + 推导出 + Object (Formula/Equation).
Example: 牛顿推导出了万有引力定律。(Newton derived the law of universal gravitation.)
Pattern 2: Logical Deduction: 根据 (Based on) + Premises + 推导 + Conclusion.
Example: 根据现有的证据，我们可以推导出结论。(Based on existing evidence, we can derive a conclusion.)

这个数学模型的推导过程非常复杂。(The derivation process of this mathematical model is very complex.)

Note that in the sentence above, 推导 acts as an attributive modifying '过程' (process). This is a very frequent usage. You can also use it in a passive sense with '被' (bèi), though it is less common: '这个公式是被推导出来的' (This formula was derived). Another important nuance is the difference between 推导 and 推理. While 推理 refers to the general act of reasoning, 推导 specifically emphasizes the 'derivation' of a specific result, often step-by-step. If you are solving a puzzle, you are 推理; if you are writing out the steps to prove a geometric theorem, you are 推导.

In professional writing, you might see 推导 paired with adverbs like 严密地 (rigorously) or 逻辑地 (logically). For example: '作者严密地推导了文章的核心论点' (The author rigorously derived the core argument of the article). This highlights the quality of the reasoning. In the context of computer science and AI, 推导 is used to describe how an engine or algorithm reaches a decision based on input data (often translated as 'inference' in AI contexts, though 推理 is also used there). Understanding these subtle shifts in meaning across domains is key to mastering the word.

You are most likely to encounter 推导 in environments where 'truth' is sought through structured thought. The first and most obvious place is the educational system. From middle school geometry to advanced theoretical physics in university, students are constantly asked to '推导公式' (derive formulas). If you watch Chinese educational videos (like those on Bilibili), you will see teachers filling whiteboards with equations while saying, '我们现在来推导一下...' (Let's derive this for a moment...).

Academic Papers: In the 'Methodology' or 'Results' section of a Chinese research paper, the word 推导 is ubiquitous. It signals to the reader that the findings aren't just observations but are logically necessitated by the data and previous theories.
Tech and Engineering: In software engineering, particularly in algorithm design, engineers 推导 the time complexity (Big O notation) of a piece of code. It's about the logical proof of efficiency.

在辩论比赛中，选手需要通过逻辑推导来驳倒对方。(In a debate competition, contestants need to use logical deduction to refute their opponents.)

Another interesting place to hear 推导 is in detective fiction or 'script killer' (剧本杀) games, which are extremely popular in China. While players often use 推理 (reasoning), a particularly rigorous player might say, '根据目前的线索，我可以推导出凶手的动机' (Based on current clues, I can deduce/derive the killer's motive). This adds a layer of intellectual authority to their claim. In the news, you might hear it during discussions about economic forecasting. Economists 推导 future market trends based on current GDP growth, inflation rates, and geopolitical shifts. It's a word that suggests the speaker has done the 'math'—whether literal or metaphorical.

Finally, in the realm of Artificial Intelligence, the term 'Inference Engine' is often translated as 推理机, but the process of deriving a specific result from a neural network can involve 推导. As China continues to lead in STEM fields, the frequency of this word in professional media is only increasing. For a learner, mastering 推导 is a gateway to understanding how Chinese speakers structure formal arguments and validate new information.

One of the most frequent errors English speakers make with 推导 is using it too broadly for any kind of 'thinking' or 'figuring out.' It is a precision tool, not a Swiss Army knife. A common mistake is confusing 推导 with 推理 (tuīlǐ). While they overlap, 推理 is the general process of reasoning (like 'logic' as a concept), whereas 推导 is the specific act of deriving one thing from another, usually in a more formal or mathematical sense.

Mistake: Using it for simple guesses: Incorrect: 我推导他今天不会来。(I derived he won't come today.)
Correct: 我推测他今天不会来。(I guess/surmise he won't come today.)
Mistake: Confusing with 'Promotion' (推动): Incorrect: 我们要推导经济发展。(We need to derive economic development.)
Correct: 我们要推动经济发展。(We need to promote/push forward economic development.)

Don't use 推导 when you mean 'recommend' (推荐 - tuījiàn). They sound similar but have zero overlap in meaning.

Another error is omitting the result. 推导 is a process-oriented word, but it usually seeks an outcome. Saying just '他在推导' (He is deriving) is grammatically fine but often feels incomplete without knowing *what* he is deriving. Usually, you should specify: '他在推导一个复杂的方程' (He is deriving a complex equation). Furthermore, learners sometimes forget to use the resultative complement '出' (chū). While '推导公式' is okay, '推导出公式' sounds more natural when the derivation has been successfully completed.

Lastly, be careful with the object of the verb. You derive *abstract* things like conclusions, formulas, and laws. You cannot 推导 a person, a place, or a physical object. If you find yourself trying to translate 'I deduced that he was the thief,' use 推断 (tuīduàn - to infer/judge) or 推理出 (tuīlǐ chū - to reason out) instead. 推导 is best reserved for when there is a clear 'path' of steps, like in math or formal logic.

The Chinese language has a rich vocabulary for intellectual processes. Understanding the synonyms for 推导 helps you choose the right 'level' of logic for your sentence. The most common related words are 推理, 推断, 推测, and 演算.

推导 (tuīdǎo) vs. 推理 (tuīlǐ): 推导 is specific to deriving a formula or a formal conclusion step-by-step. 推理 is more general, referring to the whole field of logic or the act of reasoning (e.g., 'Sherlock Holmes's reasoning').
推导 (tuīdǎo) vs. 推断 (tuīduàn): 推断 focuses on the judgment or 'inference' at the end. It's often used when you make a conclusion based on clues (e.g., 'I infer he is lying'). 推导 is more about the mathematical or formal process itself.
推导 (tuīdǎo) vs. 演算 (yǎnsuàn): 演算 specifically refers to performing mathematical calculations or operations. While 推导 might involve calculations, 演算 is more about the mechanical act of computing.

推理 is the 'What,' 推导 is the 'How,' and 推断 is the 'So what?'

If you are in a more casual setting, you might use 想出来 (xiǎng chūlái - to think of) or 算出来 (suàn chūlái - to calculate). For example, '我算出了这个题的答案' (I calculated the answer to this problem) is much more natural for a student doing homework than '我推导出了答案.' Save 推导 for when you are discussing the *derivation* of the method itself.

In academic literature, you may also see 衍生 (yǎnshēng), which means 'to derive' in the sense of 'originating from' (e.g., 'a derivative product'). However, 衍生 is usually a state or a relationship, whereas 推导 is an active process of thought. By choosing between these words, you show a high level of Chinese proficiency and an understanding of the logical structures inherent in the language.

How Formal Is It?

Fun Fact

The character '推' (tuī) is also found in the famous Chinese literary anecdote '推敲' (tuīqiāo), which refers to a poet debating whether to use the word 'push' or 'knock.' This shows the character's long history with careful choice and logic.

Pronunciation Guide

UK /tweɪ dɑːʊ/

US /tweɪ daʊ/

Primary stress on the first syllable '推' (tuī).

Rhymes With

追 (zhuī) 归 (guī) 早 (zǎo) 表 (biǎo) 考 (kǎo) 跑 (pǎo) 找 (zhǎo) 草 (cǎo)

Common Errors

Pronouncing 'tui' as 'too-ee' (it should be a single gliding sound).
Getting the tones wrong: 'tuīdǎo' (1st, 3rd) is often mispronounced as 'tuìdào' (4th, 4th).
Confusing 'dao' (3rd tone) with 'dao' (4th tone, meaning road/way).
Softening the 't' in 'tui' too much; it should be aspirated.
Shortening the 'ao' sound in 'dao'.

Difficulty Rating

Reading 4/5

High B1 level. Frequent in textbooks and formal articles.

Writing 5/5

Requires understanding of formal structures like '根据' and resultative complements.

Speaking 6/5

Rarely used in daily speech; sounds very formal.

Listening 4/5

Easily recognized in academic or professional lectures.

What to Learn Next

Prerequisites

推 (tuī) 导 (dǎo) 逻辑 (luójí) 公式 (gōngshì) 根据 (gēnjù)

Learn Next

演绎 (yǎnyì) 归纳 (guīnà) 公理 (gōnglǐ) 定理 (dìnglǐ) 假设 (jiǎshè)

Advanced

认识论 (epistemology) 形式逻辑 (formal logic) 推演 (simulation/deduction) 演算 (calculation)

Grammar to Know

Resultative Complements (出/出来)

他推导出(来)了答案。

Prepositional Phrases with '根据'

根据原理推导公式。

Passive Voice with '被'

结论被推导出来了。

Nominalization with '的'

推导的过程很长。

Using '由' for Source

由公理推导定理。

Examples by Level

老师推导这个公式。

The teacher derives this formula.

Simple Subject-Verb-Object.

他在本子上推导。

He is deriving (it) in his notebook.

Using '在' for location.

推导并不难。

Deriving is not hard.

Verb as a subject.

我们要学习推导。

We need to learn how to derive.

Verb following '学习'.

公式推导完了。

The formula derivation is finished.

Resultative complement '完了'.

请看这个推导。

Please look at this derivation.

Verb used as a noun.

他在推导1加1。

He is deriving 1 plus 1.

Present continuous action.

推导需要时间。

Deriving takes time.

Abstract subject.

根据第一步推导第二步。

Derive the second step based on the first step.

Using '根据' (based on).

你可以推导出来吗？

Can you derive it (out)?

Potential complement '出来'.

我们一起推导这个结果。

Let's derive this result together.

'一起' (together) before the verb.

推导的过程很有趣。

The derivation process is very interesting.

Modifying '过程' (process).

不要只看答案，要看推导。

Don't just look at the answer; look at the derivation.

Contrastive sentence structure.

他在黑板上推导几何题。

He is deriving a geometry problem on the blackboard.

Specific object '几何题'.

这个公式是怎么推导的？

How was this formula derived?

'是...的' structure for emphasis.

我推导出了正确的结论。

I derived the correct conclusion.

Resultative complement '出'.

逻辑推导是科学的基础。

Logical derivation is the foundation of science.

Noun phrase '逻辑推导'.

通过实验，我们推导出了新规律。

Through experiments, we derived new laws.

Using '通过' (through) for method.

这篇文章推导出了一个意外的结论。

This article derived an unexpected conclusion.

Transitive use with an abstract object.

我们需要更严密的推导。

We need a more rigorous derivation.

Adjective '严密' modifying the noun.

你能给我演示一下推导过程吗？

Can you demonstrate the derivation process for me?

'演示' (demonstrate) + '推导过程'.

这个结论是从前提推导出来的。

This conclusion was derived from premises.

Passive-like '从...出来的' structure.

数学家喜欢推导各种复杂的方程。

Mathematicians like to derive all sorts of complex equations.

Plurality expressed by '各种'.

他的推导逻辑非常清晰。

His derivation logic is very clear.

Possessive '他的' modifying the noun phrase.

由基本公理推导定理是数学的核心。

Deriving theorems from basic axioms is the core of mathematics.

Using '由...推导' (derive from).

研究人员推导出了经济增长的模型。

Researchers derived a model for economic growth.

Compound object '经济增长的模型'.

这种方法可以用来推导未知的参数。

This method can be used to derive unknown parameters.

'用来' (used to) + verb.

如果不仔细推导，很容易出错。

Without careful derivation, it's easy to make mistakes.

Conditional '如果...就' (implicit).

该论文详细推导了量子纠缠的性质。

The paper derived the properties of quantum entanglement in detail.

Adverbial '详细' (in detail).

逻辑上，我们可以推导出这个必然结果。

Logically, we can derive this inevitable result.

Adverbial '逻辑上' (logically).

推导过程中每一个环节都至关重要。

Every link in the derivation process is crucial.

'至关重要' (crucial) as a predicate.

他花了整整一个下午推导那个几何证明。

He spent an entire afternoon deriving that geometric proof.

Time duration '整整一个下午'.

通过严谨的数学推导，该假说得到了验证。

Through rigorous mathematical derivation, the hypothesis was verified.

Formal passive '得到' construction.

这种推导方式在哲学探讨中十分常见。

This mode of derivation is very common in philosophical inquiries.

Noun phrase '推导方式'.

我们不能仅凭直觉，而要依靠逻辑推导。

We cannot rely solely on intuition, but must rely on logical derivation.

'不能...而要...' (cannot... but must...).

该算法的推导基于概率论的基本原理。

The derivation of this algorithm is based on the fundamental principles of probability theory.

'基于' (based on) as a formal preposition.

这一结论的推导过程引发了广泛的学术争论。

The derivation process of this conclusion sparked extensive academic debate.

Complex subject with '引发' (trigger).

物理学家试图从弦理论推导出万有理论。

Physicists are trying to derive the Theory of Everything from string theory.

'试图' (attempt) + '从...推导出'.

他在辩论中巧妙地推导出了对方逻辑的矛盾。

In the debate, he cleverly derived the contradictions in his opponent's logic.

Adverb '巧妙地' (cleverly).

推导的严密性决定了研究的可靠性。

The rigor of the derivation determines the reliability of the research.

Abstract nouns ending in '性' (ness/ity).

该定理的推导不仅是技术的胜利，更是思想的飞跃。

The derivation of this theorem is not only a technical victory but also a leap of thought.

'不仅是...更是...' structure.

在认识论层面，推导是获取间接知识的主要途径。

At the epistemological level, derivation is the primary way to acquire indirect knowledge.

Highly formal academic register.

作者在文中对资本主义的崩溃进行了逻辑推导。

The author conducted a logical derivation of the collapse of capitalism in the text.

'对...进行...' (to carry out... on...).

任何推导都无法超越其公理系统所设定的界限。

No derivation can transcend the boundaries set by its axiomatic system.

Use of '任何...都无法' (nothing can...).

这种递归推导揭示了自然界中分形结构的本质。

This recursive derivation reveals the essence of fractal structures in nature.

Technical scientific vocabulary.

该法律条文的适用可以通过法理推导来确定。

The applicability of this legal provision can be determined through jurisprudential derivation.

Legal terminology '法理推导'.

我们在推导过程中必须排除一切主观偏见的干扰。

We must exclude all interference from subjective bias in the derivation process.

'排除...干扰' (exclude interference).

通过对历史数据的回归分析，研究者推导出了这一演化模型。

Through regression analysis of historical data, the researchers derived this evolutionary model.

Complex scientific methodology description.

Synonyms

推断演绎演算求证

Antonyms

直觉猜测

Common Collocations

推导公式

逻辑推导

推导过程

数学推导

推导出结论

严密推导

反向推导

理论推导

公式推导

递归推导

Common Phrases

推导出来

— To successfully derive something.

他终于把那个难题推导出来了。

由此推导

— Deriving from this (point).

由此推导，我们可以发现新的问题。

重新推导

— To re-derive or derive again.

如果结果不对，你需要重新推导。

逐步推导

— To derive step-by-step.

请逐步推导这个方程。

逻辑严密的推导

— A logically rigorous derivation.

这是一篇逻辑严密的推导文章。

初步推导

— A preliminary derivation.

根据初步推导，我们有了大概的方向。

试图推导

— To attempt to derive.

科学家试图推导宇宙的起源。

无法推导

— Cannot be derived.

这个结论从目前的数据中无法推导。

错误推导

— Incorrect derivation.

由于一个细节错误，导致了错误推导。

公式的推导

— The derivation of the formula.

公式的推导过程写在黑板上了。

Often Confused With

推导 vs 推理

Reasoning in general. Use '推理' for detectives, '推导' for math.

推导 vs 推荐

To recommend. Sounds similar but totally different meaning.

推导 vs 推动

To promote or push forward a physical object or social movement.

Idioms & Expressions

"顺理成章"

— To follow logically; to be natural and reasonable. Related because a good '推导' should be '顺理成章'.

只要逻辑正确，结论自然顺理成章。

Formal/Literary

"循序渐进"

— To proceed step by step. Describes the ideal process of '推导'.

学习推导公式需要循序渐进。

General

"举一反三"

— To infer other things from one fact. A higher form of logical '推导'.

他学会了这个公式，就能举一反三推导出其他的。

Education

"顺藤摸瓜"

— To follow a clue to the end (like following a vine to the melon). A metaphorical '推导'.

警察根据线索顺藤摸瓜，推导出了真相。

Informal

"丝丝入扣"

— Closely knit; logically flawless. Often used to describe a great '推导'.

他的逻辑推导丝丝入扣，令人信服。

Literary

"自圆其说"

— To make one's argument consistent. Important in logical '推导'.

你的推导必须能够自圆其说。

Neutral

"洞若观火"

— To see things as clearly as looking at a fire. The result of a clear '推导'.

经过一番推导，他对此事洞若观火。

Literary

"水到渠成"

— When conditions are ripe, success comes naturally. Used for a conclusion reached by '推导'.

逻辑通了，结论自然水到渠成。

General

"条理清晰"

— Well-organized and clear. Essential for any '推导过程'.

他的推导报告条理清晰。

Neutral

"不攻自破"

— To collapse of itself. Used for a false '推导' or argument.

由于逻辑错误，他的推导不攻自破。

Formal

Easily Confused

推导 vs 推理

Both involve logic.

推理 is the general process of reasoning; 推导 is the specific derivation of a result.

他在进行逻辑推理。 vs. 他在推导物理公式。

推导 vs 推断

Both involve reaching a conclusion.

推断 is often a judgment based on clues; 推导 is a systematic derivation.

我推断他没说实话。 vs. 我推导出了这个结论。

推导 vs 演算

Both used in math.

演算 is the mechanical calculation; 推导 is the logical reasoning behind the formula.

他在纸上演算。 vs. 他在推导公式。

推导 vs 推演

Both involve logical steps.

推演 is often for simulations or scenarios (wargaming); 推导 is for formulas/laws.

专家对战局进行了推演。 vs. 专家推导出了模型。

推导 vs 推测

Both involve guessing/logic.

推测 is more like 'surmise' or 'guess'; 推导 is rigorous derivation.

这只是我的推测。 vs. 这是严密的推导。

Sentence Patterns

S + V + O

我推导公式。

根据 + Premise + 推导

根据第一步推导第二步。

S + 推导 + 出 + O

他推导出了结论。

S + 严密地 + 推导

科学家严密地推导了定律。

由...推导至...

由基本假设推导至最终模型。

进行 + 逻辑推导

对该命题进行逻辑推导。

推导 + 过程

推导过程很复杂。

试图 + 推导

他们试图推导新规律。

Word Family

Nouns

推导过程 (derivation process)

推导式 (derivation formula)

逻辑推导 (logical derivation)

Verbs

推导 (to derive)

推导出 (to successfully derive)

Adjectives

推导性的 (derivative/deductive)

推理 (reasoning)

推断 (inference)

引导 (guide)

推辞 (decline)

导师 (tutor/advisor)

How to Use It

frequency

High in STEM fields, medium in general formal writing.

Common Mistakes

Using '推导' for guessing a friend's mood. → 我推测/推断他心情不好。
'推导' is too formal and mathematical for social situations.
Using '推导' as 'recommend'. → 我推荐你买这本书。
Confusing '推导' (tuīdǎo) with '推荐' (tuījiàn).
Saying '推导经济'. → 推动经济发展。
Confusing '推导' (derive) with '推动' (promote/push forward).
Using '推导' for a physical object. → 我算出了桌子的长度。
You derive formulas or conclusions, you don't 'derive' a physical measurement.
Omitting '出' in 'I derived the formula'. → 我推导出了公式。
Without '出', it sounds like the action is in progress rather than completed.

Tips

Pair with '根据'

Always mention what you are basing your derivation on using '根据' (based on). It makes your sentence complete.

Use in STEM

If you are a student or professional in science, technology, engineering, or math, this is a must-know word.

Resultative Complement

Remember to add '出' or '出来' when you have successfully finished the derivation.

Master the Third Tone

Ensure 'dǎo' is a clear dipping-rising tone, or it might be confused with other words like 'dào' (road).

Learn with '过程'

The phrase '推导过程' (derivation process) is so common it's almost like a single word. Learn them together.

Formal Situations

Use '推导' to sound more intelligent and precise in formal writing or debates.

Don't confuse with '推理'

Use '推理' for general logic and '推导' for specific derivations of formulas or results.

Look for it in Proofs

When reading a mathematical proof in Chinese, '推导' will often signal the start of the core logic.

Describe Logic

Use it as an adjective: '推导性的' (deductive) to describe a method or approach.

Mental Exercises

Think of '推导' as the 'adventure' of getting to an answer. It’s not about the destination, but the steps!

Memorize It

Mnemonic

Think of 'TUI' as 'Pushing' a train and 'DAO' as the 'Track' (guide). You are pushing the logic along the track to reach the station (conclusion).

Visual Association

Imagine a scientist pushing a giant '1+1' block along a path that leads to a '2' block. The path is the '导'.

Word Web

推 (push) 导 (lead) 公式 (formula) 逻辑 (logic) 证明 (proof) 数学 (math) 结论 (conclusion) 过程 (process)

Challenge

Try to explain a simple concept (like why 2x2=4) using the word '推导' in a Chinese sentence. Focus on the steps!

Word Origin

The word '推导' is a compound of two ancient Chinese characters. '推' (tuī) originally depicted a hand pushing something forward, evolving into metaphorical meanings like 'to infer' or 'to promote.' '导' (dǎo) originally meant to lead or guide someone along a path, often associated with a leader or a road.

Original meaning: To push and lead; to guide a thought process forward along a logical path.

Sino-Tibetan

Cultural Context

No specific sensitivities; this is a neutral, intellectual term.

In English, 'derive' is mostly academic. In Chinese, '推导' is similarly formal but is a standard part of every high schooler's vocabulary.

Mathematical proofs in the 'Nine Chapters on the Mathematical Art' (九章算术). Modern Chinese physics papers on the 'Yang-Mills' theory. Detective stories like 'The Devotion of Suspect X' (popular in China).

Practice in Real Life

Real-World Contexts

Mathematics Class

推导公式
推导过程
几何推导
代数推导

Scientific Research

理论推导
实验推导
模型推导
推导出新定律

Logical Debates

逻辑推导
严密推导
错误推导
推导出的结论

Programming/AI

自动推导
推导引擎
算法推导
类型推导

Detective Work

线索推导
动机推导
反向推导
事实推导

Conversation Starters

"你觉得这个公式的推导过程难吗？"

"我们能从这些数据中推导出什么结论？"

"你最喜欢的数学推导是哪一个？"

"在你的工作中，逻辑推导重要吗？"

"他是怎么推导出那个秘密的？"

Journal Prompts

描述一次你通过逻辑推导解决问题的经历。

你认为直觉和逻辑推导哪个在科学研究中更重要？

写一段话，尝试推导出一个你对未来的看法。

反思一下，为什么很多学生觉得公式推导很枯燥？

如果人工智能可以完成所有的逻辑推导，人类还需要学习逻辑吗？

Frequently Asked Questions

10 questions

Not really. '推导' is too formal for a puzzle. Use '推理' (reasoning) or '想' (think) instead. '推导' implies a more academic or mathematical derivation.

'推导' is the action of deriving. '推导出来' emphasizes the successful completion of the action and the resulting conclusion or formula. For example, '他在推导' (He is deriving) vs. '他推导出来了' (He derived it).

Rarely. It's mostly found in schools, research, or very formal debates. If you use it while shopping, people will think you're joking or being very strange.

Yes, it can. For example, in '这个推导很精彩' (This derivation is brilliant), '推导' acts as a noun.

The most natural way is '推导出结论' (tuīdǎo chū jiélùn).

Yes, if you are explaining how you reached a certain projection or financial model, '推导' is a very professional word to use.

No, it can also involve formal logic or philosophical arguments, but math is the most common context.

There isn't a single direct opposite, but '假设' (hypothesis/assume) is often the starting point that precedes a derivation, and '臆断' (arbitrary judgment) is the opposite of logical derivation.

Yes, '推导' is very close to 'deduction' (演绎推导) in a formal logical sense.

Yes, it is used to describe how models derive answers, though '推理' (inference) is also very common in AI contexts.