Can you use the mana from Dark Ritual to pay for a commander's commander tax?

Dark Ritual produces three black mana when it resolves. That mana goes into your mana pool and can be spent on anything that requires black mana or generic mana, with no restrictions based on the source of the mana.

The commander tax (formally called the 'additional cost' from Commander rule 903.8) simply increases the generic mana component of your commander's casting cost by {2} for each previous time it was cast from the command zone. There is nothing about this additional cost that restricts which mana sources can pay for it.

Mana in your pool has no memory of where it came from once it is produced (CR 106.4). So black mana from Dark Ritual is identical to black mana from a Swamp or any other source once it enters your mana pool.

Example: Your commander costs {3}{B}{B} and has been cast once before, so the commander tax adds {2}, making the total {5}{B}{B}. You cast Dark Ritual for {B}{B}{B}. You can use all three black mana from Dark Ritual toward that {5}{B}{B} cost — paying {B}{B} of the colored requirement and {1} of the generic — and cover the rest with other mana sources.

There are no Commander format rules that restrict which mana sources can pay the commander tax. As long as the mana is the right color (or generic), it works (CR 106.1, 903.8).