Your diagram looks suspiciously like it is saying that "the very orange kitten" is a determinative phrase (DP) not a noun phrase NP). Is that what you've been taught?

English Teacher
Your diagram looks suspiciously like it is saying that "the very orange kitten" is a determinative phrase (DP) not a noun phrase NP). Is that what you've been taught?
Yes.
According to Andrew Carnie (Syntax, a Generative Introduction; third edition), that's a determiner phrase, apparently because it starts with a determiner.
Carnie explains that in modern x-bar theories, a sentence is presented as TP which includes a DP and a VP under a V' node. And sometimes a CP is needed under a VP, like when you say "My mother said that he helped people a lot". Here "my mother" is a DP. "that he helped…" is a CP.
By the way, my question is how to draw a tree for "the paw of the kitten"?