rapide
rapidly
Happening very quickly and within a short time; taking place rapidly. Often used to describe a change.
Die Zahl der Nutzer ist in den letzten Wochen rapide angestiegen.
The number of users has risen rapidly in recent weeks.

rapid
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rapidly
Happening very quickly and within a short time; taking place rapidly. Often used to describe a change.
Die Zahl der Nutzer ist in den letzten Wochen rapide angestiegen.
The number of users has risen rapidly in recent weeks.

The word 'rapide' (rapidly) is almost always used as an adverb to describe a verb of change. It then stands directly with the verb and is not declined.
Die Technologie hat sich in den letzten Jahren rapide entwickelt.
Technology has developed rapidly in recent years.
'Rapide' (rapidly) describes a fast change. It is often combined with verbs such as 'ansteigen' (to rise), 'sinken' (to fall), 'wachsen' (to grow), 'abnehmen' (to decrease), or 'sich verschlechtern' (to worsen).
Die Zahl der Arbeitslosen ist im letzten Quartal rapide gesunken.
The number of unemployed people fell rapidly in the last quarter.
'Rapide' (rapidly) is a word used in written language or a more formal style. It is often found in news reports, reports, or academic texts.
Der Zustand des Patienten verschlechterte sich rapide.
The patient's condition worsened rapidly.
fast / quick
'schnell' and 'rapide' both describe that something happens in a short time. 'schnell' is the normal everyday word and fits movements, actions, and many situations: 'ein schneller Zug' (a fast train), 'schnell antworten' (to answer quickly), 'schnell gehen' (to walk quickly / to leave quickly). 'rapide' sounds somewhat more formal and is used especially often for major changes, for example when prices, numbers, or temperatures rise or fall sharply within a short time. In everyday language, 'schnell' is usually more natural; 'rapide' fits better when you want to emphasize a clear development.

Nach der neuen Werbung steigen die Verkaufszahlen rapide.
After the new advertisement, sales figures are rising rapidly.
Sie läuft schnell zur Haltestelle, weil der Bus gleich kommt.
She runs quickly to the bus stop because the bus is coming any minute.