demonstrate

To show how to use (something).transitive

• Can you demonstrate the new tools for us?

To show the steps taken to create a logical argument or equation.

To participate in or organize a demonstration.intransitive

• Those people outside are demonstrating against the election results.

To show, display, or present; to prove or make evidenttransitive

• The debate was not long on policy, as questions about the Affordable Care Act and the war in Syria demonstrated.
• "What we are trying to demonstrate is that freight lines at lower speeds can be electrified much more cheaply. […]"