is derived below

USAGE SUMMARY

The phrase "is derived below" is correct and usable in written English.
It can be used when indicating that information or a conclusion will be provided in the following text or section. Example: "The formula for calculating the area of a circle is derived below for clarity."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

7 human-written examples

The expression of the estimator is derived below.

EURASIP Journal on Advances in Signal Processing

Here, an alternative solution proposed is to use its an upper bound, which is derived below.

EURASIP Journal on Wireless Communications and Networking

The probability of error is derived below based on the probabilities in Eqs.

EURASIP Journal on Wireless Communications and Networking

When the harvesting problems are considered, the corresponding average population level is derived below.

Advances in Difference Equations

Thus, another form of PTP and PTF as a function of F0 is derived below.

Plosone

This is derived below using the delta method.

BMC Medical Research Methodology

Human-verified similar examples from authoritative sources

Similar Expressions

53 human-written examples

The parameters β and δ depend on t and are derived below.

Journal of Mathematics in Industry

The conditional mean and variance of the state process (r_k) are derived below.

Journal of Big Data

Additionally, energy bounds are derived below which it can be guaranteed that no fixed-point exists.

Chemical Engineering Science

For toxicants, a threshold exposure level can be derived, below which it is assumed there is no statistically significant adverse effect to human health.

Nanoscale Research Letters

Afterward, the results of the multiplications of two matrices, ( c ( 0 ) ) H F ~ m H F ~ m c ( 0 ) and ( c ( 0 ) ) H F ~ m H c ( 0 ) ( c ( 0 ) ) H F ~ m c ( 0 ), are derived below.

EURASIP Journal on Wireless Communications and Networking

Expert writing Tips

Best practice

When using "is derived below", ensure that the derivation is clearly and logically presented in the subsequent section. Provide sufficient context and steps to allow the reader to follow the process easily.

Common error

Avoid using "is derived below" if the derivation is not explicitly shown or is only vaguely referenced later. Ensure the derivation is present and clearly linked to the initial statement.

Linguistic Context

The phrase "is derived below" serves as a transitional marker in writing. It indicates that the subsequent text will provide a logical or mathematical derivation of a concept, formula, or result. As Ludwig AI indicates, this phrase is typically used to prepare the reader for a detailed explanation that is to follow.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

In summary, the phrase "is derived below" is a functional marker used to signal that a logical or mathematical derivation will follow. According to Ludwig AI, this phrase is grammatically correct and most frequently used in academic and scientific writing. When employing this phrase, it's essential to ensure that the derivation is explicitly presented to avoid misleading the reader. As such, while useful in academic contexts, writers should note that this phrase may need rephrasing for more general purposes.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

is described in the coming section

This sentence is very similar to the main query, but slightly more colloquial.

is explained subsequently

Replaces 'derived' with 'explained' and 'below' with 'subsequently', indicating a focus on clarification later in the text.

is shown in detail later

Emphasizes the detailed presentation that will follow, rather than the act of derivation.

is calculated further down

Focuses specifically on calculation and uses a more informal directional indicator.

is obtained in the next section

Highlights that the information is 'obtained' not 'derived', with a precise location.

is determined hereinafter

A more formal alternative, 'hereinafter' specifies later in this document.

will be deduced later on

Uses 'deduced' to convey a logical conclusion and a more casual 'later on'.

is formulated in what follows

Indicates a more structured formulation will be presented.

is solved in the following steps

Specific to problem-solving contexts; it explains how a matter has been solved.

is the result of what follows

Focuses on the 'result' that the reader can find later on the text, and is a more sophisticated alternative.

FAQs

How can I use "is derived below" in a sentence?

Use "is derived below" to signal that a formula, concept, or result will be mathematically or logically derived in the following text. For example, "The equation for calculating the optimal value is derived below".

What phrases are similar to "is derived below"?

Similar phrases include "is explained below", "is shown below", or "is calculated below", depending on the specific context.

Is it appropriate to use "is derived below" in formal writing?

Yes, "is derived below" is suitable for formal writing, particularly in scientific, mathematical, and technical contexts where derivations are common. However, use more formal alternatives like "is determined hereinafter" for extremely formal contexts.

What's the difference between "is derived below" and "is explained below"?

"Is derived below" implies a mathematical or logical deduction process will be shown. "Is explained below" suggests a more general clarification or description will follow. Use "is derived below" when a step-by-step breakdown leading to a conclusion is presented; otherwise, use "is explained below".