If you lose one engine during takeoff in a multi-engine aircraft, you're trained to follow a standard emergency procedure: Pitch for Vy, use bank and rudder for zero side slip, mixture full rich, props full forward, power full forward, gear and flaps up, and then run an emergency checklist for one engine failure.
When one engine failure happens in a modern jetliner, what do the pilots do? Do they engage the autopilot right away so that the computer can take care of pitch, bank, and rudder for the best performance for a single engine operation? Or do they basically follow the same procedure as the one written above, which is used by GA multi-engine pilots?