de-rated take off is one where the engine power is reduced in hotter climates?
Not quite right, we operate in a summer environment where temperatures of 40-50C exist. We dont reduce the engine power because of these temperatures, in fact we generally seek the highest installed engine power available.
However, when the takeoff weight is not limited, we have the ability to reduce takeoff thrust, we do this by fooling the engine into thinking that the outside air temperature its hotter than it actually is, ie, its 45c and we tell the engine that its 50c, the power delivered is therefore less than it would be at 45c... hence reduced.
Make sense?
Mutt