obtained by derivation

USAGE SUMMARY

The phrase "obtained by derivation" is correct and usable in written English.
It can be used in contexts where you are discussing something that has been acquired or developed through a process of derivation, such as in mathematics, linguistics, or logic. Example: "The formula for the area of a circle is obtained by derivation from the principles of geometry."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

Absolute consumption and production rates were obtained by derivation of the respective fitting with the maxima indicated in Table 1.

AMB Express

The final patterns which are representing an average rather than the most typical motifs for sequences of interest, would be obtained by derivation of complete matrices of bendability.

BMC Genomics

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

For the continuous-time optimization problem, the corresponding variational inequality is usually obtained by formal derivation (not strictly derived).

Journal of Inequalities and Applications

Next, the criterion for uncertain nonlinear systems with parameter uncertainties is obtained by simple derivation.

Applied Mathematics and Computation

Next, the delay-dependent criterion for uncertain fuzzy systems has been obtained by simple derivation.

Chaos, Solitons & Fractals

Secondly, the LSF in the pixel level was obtained by the derivation of ESF.

EURASIP Journal on Advances in Signal Processing

The theoretical relationship among the pulse number, the pulse repetition frequency, the pulse width and the thermal burnout power threshold is obtained by theoretical derivation.

Microelectronics Reliability

The model structure is obtained by first principles derivation, and the model parameters are determined by direct measurement and system identification.

Control Engineering Practice

Moreover, it is also reported in this list if the mentioned state is obtained by calling or by derivation from the reference.

BMC Genomics

Our results have an immediate clinical implication in situations when predicted outcomes in CPR validation studies are lacking or deficient by describing how such predictions can be obtained by everyone using the derivation study alone, without any need for highly specialized knowledge or sophisticated statistics.

Clinical Epidemiology

Using the derivation obtained by Nowak et al. (2004), the rate of TSG inactivation is as follows: Finally, we assume that the rate of TSG inactivation includes both the emergence of cells with inactivated TSGs as well as their fixation in cell population, even if each mutation does not lead necessarily to fixation (Durrett and Schmidt 2008).

Evolutionary Applications

Expert writing Tips

Best practice

When using "obtained by derivation", ensure the context clearly explains what was derived from what, clarifying the process of obtaining the result.

Common error

Avoid using "obtained by derivation" without specifying the original source or method of derivation. Be explicit about what was derived from what to avoid ambiguity.

Linguistic Context

The phrase "obtained by derivation" functions as a passive construction indicating how a result or piece of information was acquired. It emphasizes the process of derivation as the means of obtaining something, as shown in Ludwig's examples.

Expression frequency: Rare

Frequent in

Science

80%

Formal & Business

10%

Encyclopedias

5%

Less common in

News & Media

2%

Wiki

2%

Reference

1%

Ludwig's WRAP-UP

In summary, the phrase "obtained by derivation" is a grammatically correct passive construction predominantly used in formal and scientific contexts. Ludwig AI analysis reveals that it signifies that a result or conclusion was achieved through a specific, often mathematical or logical, process. While it is not a very common phrase, when used, it is crucial to clearly specify the source and method of derivation for clarity. Consider using alternatives like "derived from" or "calculated from" to tailor the expression to the context. Ludwig confirms that this phrase is appropriate for technical writing where transparency and methodological rigor are important.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

derived through calculation

Changes the verb and emphasizes the mathematical or computational process.

determined analytically

Replaces "obtained" with "determined" and "derivation" with "analytically", highlighting a method of analysis.

ascertained through deduction

Substitutes "obtained" with "ascertained" and "derivation" with "deduction", focusing on a logical inference process.

found via mathematical process

Replaces "obtained" with "found" and clarifies "derivation" as a "mathematical process".

resulted from deduction

Shifts the focus to the outcome of a deductive process.

achieved by analytical method

Highlights the methodology of obtaining the result.

computed from first principles

Emphasizes a calculation based on fundamental assumptions.

deduced from established facts

Focuses on logical derivation from known information.

inferred through a process of reasoning

Highlights the active reasoning involved in the derivation.

calculated using established formulas

Focuses on the use of pre-existing equations for calculation.

FAQs

How can I use "obtained by derivation" in a sentence?

Use "obtained by derivation" when explaining that a result or conclusion was reached through a specific derivation process. For instance, "The equation was "obtained by derivation" from fundamental physical laws."

What is a good alternative to "obtained by derivation"?

Alternatives include "derived from", "calculated from", or "ascertained through deduction", depending on the specific nuance you wish to convey. The best choice depends on the context and the nature of the derivation process.

Is "obtained by derivation" formal or informal?

"Obtained by derivation" is generally considered a formal phrase, suitable for academic, scientific, or technical writing. It is less common in informal conversation.

What does "obtained by derivation" mean?

It means that a particular result, formula, or conclusion was reached or acquired through a process of derivation, typically involving logical or mathematical steps.