rasend
rapid
Moving at very high speed; extremely fast.
Mit rasender Geschwindigkeit näherte sich der Krankenwagen.
The ambulance approached at rapid speed.

rapid / furious
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rapid
Moving at very high speed; extremely fast.
Mit rasender Geschwindigkeit näherte sich der Krankenwagen.
The ambulance approached at rapid speed.

'Rasend' is the present participle of the verb 'rasen' (to speed; to rage). As an adjective, it therefore describes something that happens with extreme speed or intensity.
Der Sturm fegte mit rasender Kraft über das Land.
The storm swept across the country with tremendous force.
The context shows the meaning: in connection with movement, 'rasend' means very fast. In connection with feelings or pain, it means extremely strong. In connection with success, it is colloquial for 'enormous'.
Das Auto fuhr in rasendem Tempo die Straße entlang.
The car drove down the road at a rapid pace.
To express an extreme feeling, the structure 'rasend vor + [noun in the dative]' is often used. Alternatively, it can also stand directly before an adjective.
Er war rasend vor Eifersucht.
He was furious with jealousy.
In the meaning 'very great' or 'enormous', 'rasend' is used mainly colloquially. Typical combinations are 'ein rasender Erfolg' (a tremendous success) or 'rasend beliebt sein' (to be extremely popular).
Sein erstes Buch hatte einen rasenden Erfolg.
His first book was a tremendous success.
fast / quick
'schnell' and 'rasend' can both describe a very high speed. 'schnell' is neutral and fits people, vehicles, tasks, or processes. 'rasend' is much stronger and often sounds more dramatic. It is used especially when something is moving extremely fast or when you want to emphasize the speed strongly. In many everyday sentences, you simply say 'schnell'. 'rasend' fits more with strong images such as a car, train, or pace.

Der Zug fuhr rasend durch den Bahnhof, ohne anzuhalten.
The train sped through the station without stopping.
Könnt ihr bitte schnell die Fenster schließen?
Could you please close the windows quickly?