Does first strike damage resolve before deathtouch kills the blocking creature?

Combat damage is divided into two steps when any creature has first strike or double strike. In the first combat damage step, only creatures with first strike or double strike deal their damage (CR 510.1). In the second step, creatures with neither ability deal their damage (CR 510.5). This means a first strike attacker and a deathtouch blocker do not deal damage at the same time by default.

Deathtouch causes any amount of damage dealt by that creature to be considered lethal (CR 702.2b). However, deathtouch only matters when the creature actually deals damage. If the deathtouch creature is destroyed before the second combat damage step, it never gets to deal its damage at all.

State-based actions are checked after the first combat damage step (CR 704.3). If the first strike damage is lethal, the blocking deathtouch creature is put into the graveyard before the second combat damage step begins. It therefore never deals its deathtouch damage to the attacker.

Concrete example: Your 2/2 creature with first strike attacks. Your opponent blocks with a 1/1 creature with deathtouch. In the first damage step, your 2/2 deals 2 damage to the 1/1, which is lethal. State-based actions destroy the 1/1. In the second damage step, the 1/1 is gone and deals no damage — your 2/2 survives unharmed.

Note: if the blocking creature also has first strike or double strike, both creatures deal damage simultaneously in the first step, and the deathtouch creature's damage would be lethal to your attacker (CR 510.1).