And if the engine failure occurs shortly after V1 with a good spread of 5-15 knots between V1 and VR, then expect a significantly heavier than normal pull force on the control column at VR. This is because the stabiliser trim setting from the load sheet is designed to give you an in-trim stick force at a two-engine V2+15 knots.
With an engine failure, the vertical vector of engine thrust is effectively halved thus giving the appearance and feel of a nose heavy rotation. Coupled with the natural tendency for the 737 rotation forces to hesitate on passing ten degrees of body angle due to the tailplane lowering into ground effect, the end result is that you need to hold a strong back pressure to rotate to 13 degrees body angle for the initial fly-away on one engine. Use of early stab trim may be needed after gear up. Often see pilots fly back onto the runway momentarily when rotating with engine failure at VI because the stick force surprised them and they stop rotating at 8-10 degrees. And don't ask for gear up until positive rate of climb on altimeter - not IVSI. See Boeing 737 FCTM.
PS. If the flight director needles spook you after coping with initial engine failure and their two needles are dancing around the ADI then avoid chasing the needles. Best thing is to quickly switch your scan to the standby ADI which is a basic artificial horizon unencumbered by FD needles and use the standby ADI as a raw data means of keeping wings level. Once you have the climb-out under control wings level on one engine, then shift your scan back from the standby ADI to the main ADI flight director needles which by then will hopefully be centred. That said, this does not necessarily apply to the first officer handling from RH seat as the standby ADI has parallax error.