Is it grammatically correct to say:
"Подпишись, чтобы не пропустить новых видео"
or should I say:
"Подпишись, чтобы не пропустить новыe видео"?
Please, instead of just saying which option is right, provide some explanation and sources.
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I think that the problem can be restated as whether the direct object видео should be used in genitive case or accusative case. It is not as straightforward as VaNdal tried to convince you.
Wikipedia states that the direct object is used in Russian mostly in accusative case and sometimes in genitive case after transitive verbs. Выделяют прямое дополнение — беспредложное дополнение после переходного глагола (в русском языке — в винительном, иногда в родительном падеже).
I am afraid that this is the case. Like "не пить воды" or "не видеть леса за деревьями".
This is an accusative case. "Видео" is inanimate noun. So, despite the noun itself is unchangeable you need to put the adjective in the correct form. Thus, only
"Подпишись, чтобы не пропустить новые видео" (answering the question "Что?")
is the correct option.
If you had a sentence with animate noun it would be
"Подпишись, чтобы не пропустить новых друзей" (answering the question "Кого?")
Any source of Russian grammar would work here. Like this one https://www.russianlessononline.com/accusative-case-in-russian-language/
Technically, this is an example of Caritive case, one of the additional cases. Sometimes it's identical to the Genitive and sometimes to the Accusative. Sometimes both form works. https://en.wikipedia.org/wiki/Abessive_case#See_also
For the mentioned sentences it is identical to Accusative.