To combine Boolean operators and derivatives, you need to follow some basic rules and syntax. To craft effective complex queries, use uppercase letters for Boolean operators to distinguish them from keywords or phrases. Group keywords or phrases that belong together or have the same operator using parentheses; for example, (apple OR orange) AND (juice OR smoothie). Enclose exact phrases or terms that you want to match with quotation marks; for example, "apple juice" or "Steve Jobs". Replace multiple letters at the end of a word with asterisks (*); for example, comput* will match computer, computing, computation, etc. Utilize question marks (?) to replace single letters within or at the end of a word; for example, wom?n will match woman and women but not wemon. Indicate proximity between words or phrases with symbols like NEAR, WITHIN, or ADJ; for example, apple NEAR orange will match apple and orange within a certain number of words of each other depending on the search engine. Lastly, use symbols like ~, $, or # to indicate fuzzy or approximate matches; for example, apple~ will match apple and similar words like ample, apply, etc.