For hormones that are amino acid derivatives, would thyroid hormones, or perhaps tyrosine kinase be an example of that? And could they pass through the cell membrane directly? Because I know that my textbook says that they can due to their 'small and hydrophobic nature' but in the NOB book it says that amino acid derivatives cannot pass through the plasma membrane.
Yeah, as far as I'm aware, it is amino acid derivatives.
For your second question, amino acid derivatives won't generally pass through the cell membrane like lipid-based hormones. "Small and hydrophobic" -> amino acid is not really that small, if you look at the structure of an amino acid, it contains carboxyl group, amino group, a hydrogen and a variable group, all of these can make up a fair large amount of molar mass (in the case tyrosine kinase, they are around 181.19 gmol-1, so you can imagine amino acid is actually not that small). About the "hydrophobic" nature, I don't know why your textbook call them hydrophobic but they are generally soluble in water, they can be insoluble when we place them with hydrocarbon (which is a non-polar solvent). The only case that I can think of where amino acid derivatives are not soluble in water are because of their large molar mass or the nature of the R group (but I guess we don't really need to over-complicate things for VCE). I don't know if you do Chem 3/4 or not, but if you don't and really want to know why amino acid are soluble, then look up "zwitterions" form, these might help you a bit

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Anw, in brief, I don't generally think amino acid derivatives hormones can easily pass through the cell membrane because they are generally polar and not lipophilic in nature.
Correct me if I'm wrong.