derb
coarse
Crude, vulgar, or unrefined in language, behavior, or humor.
Er ist für seine derben Witze bekannt, die nicht jeder mag.
He is known for his coarse jokes, which not everyone likes.

coarse / hearty / awesome
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coarse
Crude, vulgar, or unrefined in language, behavior, or humor.
Er ist für seine derben Witze bekannt, die nicht jeder mag.
He is known for his coarse jokes, which not everyone likes.

The word 'derb' can be evaluated very differently depending on the context. 'Eine derbe Ausdrucksweise' (coarse language) is usually negative, but 'eine derbe Mahlzeit' (a hearty meal) or 'ein derbes Konzert' (an awesome concert) are meant positively.
Sein derber Humor kommt nicht bei allen gut an.
His coarse humor does not go down well with everyone.
When 'derb' describes a crude or unrefined manner, it often refers to communication. Typical nouns are 'Witz' (joke), 'Spruch' (remark), 'Humor' (humor), or 'Ausdrucksweise' (way of speaking/language).
Er entschuldigte sich später für seinen derben Spruch.
He later apologized for his coarse remark.
In connection with food, 'derb' describes a strong, simple, and filling meal. It is often used for traditional or rustic dishes.
In der Berghütte servierte man uns eine derbe Brotzeit mit Speck.
In the mountain hut, they served us a hearty snack with bacon.
In colloquial language and youth slang, 'derb' is used as a positive adjective in the sense of 'great', 'intense', or 'cool'. In this context, it is very informal.
Die Party gestern war echt derb, wir hatten so viel Spaß!
The party yesterday was really awesome; we had so much fun!
To describe the firm and robust texture of a material, 'derb' is often combined with nouns such as 'Leder' (leather), 'Stoff' (fabric), or 'Gewebe' (woven fabric/textile).
Die Jacke ist aus einem derben Baumwollstoff gemacht und sehr widerstandsfähig.
The jacket is made of a stiff cotton fabric and is very durable.
firm / fixed
'fest' and 'derb' can both refer to material that is not soft and not easily bent. 'fest' is the normal, neutral word for solid, hard, or holding well. 'derb' sounds more specific and often describes fabric, leather, or similar materials that seem coarse, strong, and not very fine. Learners may confuse the words when talking about firm materials. In many everyday situations, 'fest' is more natural. 'derb' is more suitable when you also want to emphasize the coarse or robust quality of the material.

Für die Wanderung trägt Paul eine Jacke aus derbem Stoff.
For the hike, Paul wears a jacket made of stiff fabric.
Der neue Karton ist fest genug für die schweren Bücher.
The new cardboard box is sturdy enough for the heavy books.