If a creature has both deathtouch and lifelink and deals 1 damage to a 10-toughness creature, does it die?

Deathtouch is a static ability that modifies what counts as lethal damage. Under CR 702.2h, a creature with deathtouch deals damage that is considered lethal regardless of the amount, as long as at least 1 damage is dealt. This overrides the normal rule (CR 704.5g) that a creature is destroyed only when damage meets or exceeds its toughness.

So when your deathtouch creature deals 1 damage to a 10-toughness creature, state-based actions check at the next opportunity and see that the creature has been dealt damage by a source with deathtouch — that alone is sufficient to destroy it (CR 704.5h).

Lifelink (CR 702.15b) is also relevant here: whenever your creature deals damage, you gain that much life simultaneously. So dealing 1 damage also causes you to gain 1 life, regardless of whether it kills the defending creature or not.

Concrete example: You attack with a 1/1 Deathtouch/Lifelink Snake. Your opponent blocks with a 10/10 Golem. Combat damage is dealt — you gain 1 life (lifelink), your Snake dies (the Golem has 10 power), and the Golem is destroyed by state-based actions (deathtouch made that 1 damage lethal).

Note: deathtouch only triggers destruction through state-based actions; it does not reduce toughness. The 10-toughness creature still has 9 "unmarked" toughness, but the deathtouch rule (CR 704.5h) independently flags it for destruction.