The derivative composes of two components:
Conventionally, while the ailerons are deflected anti-symmetrically, the induced drag on both sides of the wing have the same magnitude but opposite direction. A negative yawing moment is produced due to this differential induced drag. The profile drag caused by the aileron deflection is symmetrical on both sides of the wing and thus does not create any change to the yawing moment.
A negative yawing moment due to aileron deflection is undesirable because it tends to yaw an aircraft out of an intended turn. This negative yawing moment due to aileron deflection may be eliminated by differentially deflecting the ailerons. In this case, a differential profile drag component is produced which is used to off-set the negative aileron yaw.
See Graphic .