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The phrase "derived directly from" is correct and can be used in written English.
It means that something was obtained or originated directly from something else. Example: The tree's deep roots are derived directly from the nutrients in the soil.
Exact(60)
Descriptions in other studies were either derived directly from clinicians or their derivation was not described.
derived directly from his nuclear abolitionism.
They also discovered that human genes have been derived directly from bacteria.
What happens after a war is derived directly from the way it unfolds.
In Italy two alphabets derived directly from the Greek: the Etruscan and the Messapian (Messapic).
All necessary input properties are either tabulated or derived directly from the geometrical structures.
The required capabilities are derived directly from the company's long-term business strategy.
Badminton is derived directly from poona, which was played by British army officers stationed in India in the 1860s.
The first three of these were derived directly from the Greek; the Lydian and Carian were strongly influenced by it.
Both are viviparous but differ in the amount of nutrition derived directly from the mother.
Descriptive summary statistics were derived directly from the database and using Microsoft Excel.
More suggestions(15)
diverted directly from
withdrawn directly from
arisen directly from
come directly from
characterized directly from
received directly from
retrieved directly from
deduced directly from
removed directly from
driven directly from
determined directly from
involved directly from
delivered directly from
emanated directly from
came directly from
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com