Just a question about the 木 reading. I thought the kunyomi was き and the onyomi もく/ぼく but I didn’t find anything about こ (the reading in this sentence). If anyone could explain me why…
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こ is a kunyomi for 木, but I’m not sure whether or not it’s used for anything other than the word 木の葉. Just gotta remember that that’s how it’s read in that word.
I think that’s also the reading used for 木の実, so that seems to be part of the usage pattern, and I’m sure there’s a few others I’m forgetting, but it’s not the most common reading I don’t think
こ tends to be used for older/more poetic words and phrases. The big one that comes to mind is 木漏れ日. Also things like 木霊 or 木立, etc.
Also, welcome to the forums!
Just cause no one has mentioned it yet but quite few people know it even if they haven’t noticed that they know it. Konoha village from Naruto is 木の葉.
Regular construction that just means foliage.
Ohhhh nice thank you, I would never guess that 

In the official list of joyo kanji, for 木, the kun reading こis included, but it appears indented one character to the right. It says that they are special readings, or readings with very narrow use. As examples or this reading, 木立,木陰, just the ones that have been mentioned (pag. 143).
This is a link to the official list of joyo kanji, with the last additions in 2010
It’s a pdf, difficult to use. The joyo kanji list is also in Wikipedia. It uses as source the same pdf.