To the left, I state a conventional definition of the derivative of the function in question. When x is negative as it is on the second line of the derivation, the numerator (|x + dx| - |x|) is -dx because dx is always a positive number. Thus the derivative is -1. On the third line when x is positive, this simplifies to +1.
Plate subduction occurs when two tectonic plates converge and at least one of them is an oceanic plate. Oceanic plates are formed at divergent plate boundaries from dense basaltic magma. This magma originates from the mantle beneath and fills the gap between the spreading plates.
Subduction zone volcanism occurs where two plates are converging on one another. One plate containing oceanic lithosphere descends beneath the adjacent plate, thus consuming the oceanic lithosphere into the earth's mantle. This on-going process is called subduction.