Which verb focuses on proving or making something clear through reasoning or examples?

The verb that focuses on proving or making something clear through reasoning or examples is "demonstrate." This verb emphasizes showing how something works or providing evidence or clarity about a concept, idea, or process. When someone demonstrates something, they usually present practical examples, reasoning, or visual aids to help others understand a point or see the validity of an argument.

In contrast, the other verbs encapsulate different actions. "Derive" often refers to obtaining something from a source or drawing conclusions based on prior knowledge. "Design" pertains to the creation or planning of a structure or system, focusing more on aesthetics or functionality rather than proof or clarity. "Develop" involves expanding or elaborating on an idea or concept but does not specifically concentrate on the act of proving or illustrating it effectively. Thus, "demonstrate" is the most appropriate choice as it directly relates to proving or clarifying through reasoning or examples.