I'm currently writing a little book which explains all equations that first year students will use. There is a law that requires many assumptions and I have referred the student to the page in the textbook that explains the assumptions. Is this safe to do? I'm worried that I can be charged for derivative work as I am using the textbook's explanation to help the student understand my explanation of the formula. Any comments will be appreciated.
Are you copying material from this textbook into your book? Or do you mean that you are just writing, "See page 42 of Such-and-such book"?
Usual disclaimer: I am not a lawyer. But as I understand U.S. copyright law, if you are not copying the actual words from another book, you are in no danger of violating copyright. You can certainly refer people to another book. You can rewrite the material from another book in your own words -- just make sure "your own words" are sufficiently different from the other writer's words, you can't just change two words in ten pages of text.
There is also the "fair use doctrine" that says you can quote small sections of someone else's work. The rules here are not hard and fast, but if you quote three paragraphs from a 200 page book, you are not likely to get into trouble. If you quote 100 pages word for word from a 200 page book, you are asking for trouble.
I'm currently writing a little book which explains all equations that first year students will use
A short remark before going on with the question: your claim in bold is definitely questionable.
There is a law that requires many assumptions and I have referred the student to the page in the textbook that explains the assumptions. Is this safe to do?
Yes, it is safe to do it and it is commonly done in all scientific literature. Typically one doesn't cite the page of a textbook, which can change between different printings, but the chapter or the section, which are less likely to change. So, you may write something like:
Equation (1) is valid when the following assumptions are verified [1, Sec. 4.6]:
If the equation is so common that it can be found in a large number of textbooks, you can stress this fact by writing something like:
Equation (1) is valid when the following assumptions are verified (see, e.g., [1, Sec. 4.6]):
You may want to query the publisher of the Original Textbook and see if they want to issue your guide as an Official Supplement?
I don't know what the subject is -- if it's something like Physics where these equations are now "known facts", you may be fine doing these as your own work, but if you're doing something where the choice of equations is more up for debate, then I would consult the publisher of Main Textbook.
Another route may be to link your supplement to a textbook that's more Public Domain, such as those in the Open Textbook Project, or seek for some Creative Commons ones.
(I am not a lawyer)
From your question it sounds like you are making a compilation of the equations. If you are not including any new material in your book (explanations or ideas) it is necessary that you provide a reference to all content in it.
If you provide an explanation and want your readers to refer to another textbook, then say so within your text. Most authors provide footnotes for this.
"First year students" refers to students studying what? If the contents of your book are something which will be useful for only a small group of people, it would be a better idea to publish your compilation on a blog rather than go through the laborious process of bringing out a book.