was derived by

USAGE SUMMARY

The phrase "was derived by" is correct and usable in written English.
It can be used to indicate the source or origin of something, often in academic or formal contexts. Example: "The formula for calculating the area of a circle was derived by mathematicians over centuries of study."

✓ Grammatically correct

Science

News & Media

Formal & Business

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The number was derived by simply adding together the two countries' populations.

The Guardian

That number was derived by simply adding together the two countries' populations.

The Guardian - Opinion

Surface structure of synthesized material was derived by FTIR analysis.

Journal of Alloys and Compounds

The overall influence of ACC over FEF was derived by implementing the (GACC→FEF−GFEF→ACC) equation.

Nature

A 15th-order nonlinear state equation set was derived by integrating these three subsystems.

Applied Energy

The framework was derived by literature review, design science research and evaluated via a simulation.

Environmental Modelling & Software

Divergence angle expression was derived by the geometry and spatial relationship.

Optik - International Journal for Light and Electron Optics

"The 'Let sunshine win the day' line was derived by Steve Hilton and injected into Cameron's speech at the very last minute.

The Guardian

The name was derived by Serkis from the "vivarium" of Victorian times, in which animals were kept in a semi-natural state.

The Guardian

which was derived by Novikov [1].

Boundary Value Problems

The classic model was derived by Nicholson and Bailey (1935).

Advances in Difference Equations

Expert writing Tips

Best practice

When using "was derived by", ensure that the subject is clearly defined and the source of derivation is explicitly stated to avoid ambiguity. For example, "The equation was derived by applying the principles of thermodynamics."

Common error

Avoid using "was derived by" with an unclear or ambiguous subject. For example, instead of saying "It was derived by experiments", specify what 'it' refers to: "The conclusion was derived by the experiments".

Linguistic Context

The phrase "was derived by" functions as a passive voice construction, indicating the source or method used to obtain a particular result, formula, or conclusion. As Ludwig AI states, the phrase is grammatically correct and usable in written English.

Expression frequency: Very common

Frequent in

Science

75%

News & Media

10%

Formal & Business

5%

Less common in

Wiki

5%

Academia

3%

Reference

2%

Ludwig's WRAP-UP

In summary, the phrase "was derived by" is a grammatically sound and frequently used construction to indicate the origin or methodology behind a particular result or conclusion. As confirmed by Ludwig AI, this phrase is most commonly found in scientific and academic contexts, which require precision and clarity in attributing sources. While alternatives such as "was obtained from" or "was based on" exist, "was derived by" specifically highlights a process of reasoning or calculation. For effective writing, ensure that the subject is clear and the source of derivation is explicitly stated, avoiding vagueness. By following these guidelines, writers can confidently use "was derived by" to enhance the credibility and context of their work.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

was obtained from

Focuses on the act of getting something from a source.

was sourced from

Emphasizes the origin or supplier of the element.

was developed from

Highlights the evolution or creation process.

was created by

Focuses on the act of creation and the agent responsible.

was formulated by

Indicates a structured or systematic creation.

stemmed from

Suggests that something originated or arose from a particular source.

originated from

Indicates the place or point where something began.

was based on

Highlights the foundation or groundwork upon which something is built.

resulted from

Emphasizes the outcome or consequence of something.

arose from

Suggests a gradual or natural emergence from a source.

FAQs

How can I use "was derived by" in a sentence?

Use "was derived by" to indicate the source or method through which something was obtained or developed. For example, "The formula "was derived by mathematical induction"."

What are some alternatives to "was derived by"?

You can use phrases like "was obtained from", "was based on", or "resulted from" depending on the specific nuance you want to convey.

Is it better to use "was derived by" or "was created by"?

The choice depends on the context. "Was derived by" suggests a process of reasoning or calculation, while "was created by" implies a more general act of bringing something into existence. For example, a mathematical formula might be derived, whereas a work of art is created.

What's the difference between "was derived by" and "was influenced by"?

"Was derived by" indicates a direct origin or source, suggesting a logical or procedural connection. "Was influenced by", on the other hand, suggests a less direct effect or inspiration. For example, a theory "was derived by empirical data", while an artist might be influenced by a particular movement.