deutlich
clear
Clear and easy to understand, so that it can be heard, seen, or read well.
Können Sie bitte etwas lauter und deutlicher sprechen?
Could you please speak a little louder and more clearly?

clear / clearly
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clear
Clear and easy to understand, so that it can be heard, seen, or read well.
Können Sie bitte etwas lauter und deutlicher sprechen?
Could you please speak a little louder and more clearly?

The adjective 'deutlich' (clear/clearly) is related to the verb 'deuten', which means 'zeigen' (to show) or 'interpretieren' (to interpret). So something that is 'deutlich' can be recognized or understood well.
Seine Geste war eine deutliche Ablehnung.
His gesture was a clear rejection.
'Deutlich' (clearly) can be used unchanged as an adverb to describe a verb. In this function, it answers the question 'Wie?' (How?).
Er hat seine Meinung deutlich gesagt.
He stated his opinion clearly.
As an adverb, 'deutlich' (significantly) is very often used to emphasize a difference. It then stands directly before a comparative (e.g. 'besser' (better), 'mehr' (more)) or an adjective and means 'viel' (much) or 'wesentlich' (substantially).
Seit dem Training ist sie deutlich schneller geworden.
Since the training, she has become significantly faster.
In the meaning 'klar verständlich' (clearly understandable), 'deutlich' (clear/clearly) is often connected with communication: 'deutlich sprechen' (to speak clearly), 'deutlich schreiben' (to write clearly), or to have a 'deutliche Aussprache' (clear pronunciation).
Bitte schreiben Sie Ihren Namen in deutlichen Buchstaben.
Please write your name in clear letters.
much / a lot
'viel' and 'deutlich' can both intensify a comparison. You can say that something is 'viel besser' (much better) or 'deutlich besser' (significantly better). 'viel' is very general and very natural in everyday language. 'deutlich' emphasizes that the difference is clearly noticeable and not just small. It often sounds a bit more precise, for example with results, prices, or changes. Important: in this relation, 'deutlich' is being used as an intensifier. In other sentences, 'deutlich' can also mean 'clearly audible, visible, or understandable'.

Nach der Reparatur läuft der Computer deutlich leiser.
After the repair, the computer runs significantly more quietly.
Mit deiner Hilfe geht die Arbeit viel schneller.
With your help, the work goes much faster.