I have a question regarding a/the usage. Is it correct to say: "First of all, you should specify a type of the derivative"? Am I right that "type" in this case is something unknown, generic, one of the many, so we use "a". And "derivative" is specific and is the only one in regard to the "type" (in other words, in the context of the "type", there's only one "derivatve", so we use "the"). I'm sorry if it sounds stupid or overcomplicated, but it is really hard for me to grasp these things.
First of all, you should specify the/a type of derivative.

'Derivative' does not take an article. The choice for 'type' depends on whether the possible types to be chosen from have been discussed before in the context. Presumably, there are only a few types available, and the reader and writer know what is being talked about, so there is little 'unknown, generic' about these types.
Thank you for your reply!

Why there isn't any article before "derivative"? It's adjective? If so, let's change it to some noun, "access" let it be. "a/the type of a/the access". Singular nouns can't be used without any article (or my/some/etc), aren't they? It is the second word that puzzles me the most.

Regarding "type". If it is unknown to a listener, why should we use "the" (even though there're only several types)? Reader doesn't know it. For me it is like "you can pick up a chair and sit with us at the table" -- though there're definite set of chair, we do not talk about some specific chair.
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No, it is not an adjective. The 2nd noun just doesn't take an article: a type of access, a piece of pie, a kind of fruit, the right sort of girl for me.

Reader knows it if the text has been logical. Looking at it another way, there is only one type to be chosen: the type. Please supply the preceding text that "First of all, you should specify a type of derivative" appears after..
Sorry, I forgot to provide context. For example, let it be the following: "When you first run this Emotion: computer program, you must specify a/the type of a/the access."

The 2nd noun just doesn't take an article
Well, that's confusing. My study book is R. Murphy's English Grammar In Use, and it explicitly says "you cannot use singular countable nouns alone (without a/the/my etc.)". Maybe it's because the book is about British English?

Please supply the preceding text that "First of all, you should specify a type of derivative" appears after..
Actually I didn't mean anything to be put after "derivative", it's just "type of derivative" (derivative security, economics term). Or maybe the phrase I constructed is incorrect and there must be something after it?
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It is not British English. Murphy has just simplified the rule. For species nouns (type, kind, sort, variety, etc.), we usually place determiners and other modifiers before the species noun rather than the noun following 'of': a strange kind of fish, a rare breed of dog.

Your phrase, 'a type of derivative' is fine. Use of 'a' or 'the' before 'type' is not so important here – I am sure that you can choose the appropriate one in a real context.
Mister Micawber, thanks for clarification!