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.
No, earthquakes always occur when two continental plates collide. Yes, subduction always occurs when continental plates collide. No, usually no subduction occurs when continental plates collide. Yes, subduction always occurs when oceanic plates collide.