Noise Unit,
I am still not exactly sure which part of this subject you are trying to understand here (or why), but to add to Mutt & YP’s answers:
An airline will generally operate the aircraft’s engines at the lowest derate that is practical because it puts the engines on a cheaper maintenance schedule. For instance an airline may operate its 737 fleet with engines derated to 22K in the summer when loads are higher and 20K in winter when they are lower. This may also be accompanied by a change in the declared MTOW to reduce landing & nav charges (in the winter). The different engine ratings require a whole new set of performance tables and is a big job.
Take-off Derate
The Captain may on the day decide that he either needs more power, eg to get past an obstacle (say 22K when the a/c is notified as 20K) and depending on the airline he may either have to ask his Ops for a one-off authorisation or it may just be a tech log entry. Either way he must use 22K perf data. In some rare cases he may need less power eg if he is Vmcg limited, this is usually much easier insofar as nobody needs to be asked but again you must use the perf data applicable to the engine rating.
Climb Derate
This is done almost every sector either automatically as a consequence of using an assumed temperature thrust reduction (aka Flex) or manually by selecting CLB-1 or CLB-2 in the FMC after you have cleaned up and don’t require full climb power. It is more of an airmanship thing to reduce your climb thrust to reduce engine wear (good for the company’s bills and reduces your chance of having some asymmetric practice!). NB this is not a true “derate”, just a reduction of climb thrust.
If you haven’t already seen it, I have produced a more in-depth article on this at
http://www.b737.org.uk/assumedtemp.htm This has photos of all the FMC pages used to make these selections, it is based on the 737 but is valid for all jet types.
S & L