exceeding / going out
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exceeding
Being or doing more than something; going beyond a certain framework, measure, or expectation.
Sein Engagement war weit über das normale Maß hinausgehend.
His commitment went far beyond the normal measure.
'Hinausgehend' is the present participle of the separable verb 'hinausgehen' (to go out). It is made up of the direction 'hinaus' (out of a place) and the movement 'gehen' (to go).
Der aus dem Haus hinausgehende Gast vergaß seinen Schirm.
The guest going out of the house forgot his umbrella.
In the figurative meaning, 'hinausgehend' (exceeding/going beyond) is almost always used with the preposition 'über' and an accusative object. The structure is: 'über etwas (Akk.) hinausgehend' (going beyond something).
Ihre Hilfe war weit über das normale Maß hinausgehend.
Her help went far beyond the normal measure.
The preposition 'über' almost always signals the figurative meaning ('more than'). If this preposition is missing, the literal meaning ('leaving a place') is usually meant.
Sein Interesse an dem Thema ist über eine reine Neugier hinausgehend.
His interest in the topic goes beyond mere curiosity.
additional
'zusätzlich' and 'hinausgehend' can both express that something is more than what is normal or expected. 'zusätzlich' simply means that something extra is added. 'hinausgehend' is usually used in the form 'über etwas hinausgehend' (going beyond something) and means that a framework, a measure, or an expectation is exceeded. The words can be confusing because both point to something more. In practice: for an extra thing, 'zusätzlich' is more natural; when something goes beyond a limit or a rule, 'hinausgehend' fits better.
Die Lehrerin stellt eine über den Unterricht hinausgehende Aufgabe.
The teacher assigns a task that goes beyond the lesson.
Für das Projekt bekommt er zusätzlich zwei Tage Zeit.
For the project, he gets an additional two days.