Both mean "to demolish" or "to knock down", but I believe there are some differences. What are these differences, and are they based on region or context?
"Derribar" and "derrumbar" are very close in meaning but there is a difference both in terms of lexical collocations and grammar.
"Derribar" is only used as a transitive verb, and the object can be things such as vertical structures (walls, trees), buildings, planes (e.g. during a war), or people (an opponent in a fight, a government -- in which case "derribar" is synonymous with "derrocar", i.e. "overthrow").
- derribar un árbol
- derribar una pared
- derribar un edificio
- derribar un avión
- derribar al contrincante
- derribar (a) un gobierno
"Derrumbar" can be both transitive and pronominal intransitive, the latter use (in English "collapse") being more frequent. Pronominal "derrumbarse" can refer not only to concrete things (e.g. la casa se derrumbó) but to more abstract nouns like prices, the market, hope, spirits, reputation.
- los precios / los mercados se derrumbaron
- su esperanza se derrumbó
- su ánimo se derrumbó
- su fama se derrumbó