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 meet at a convergent plate boundary (the plates are crashing into one another) and at least one of the plates is denser than the underlying mantle. If neither plate is denser than the underlying mantle the plates will create a non-volcanic mountain range like the Himalaya.
1 First, in most subduction zones, large earthquakes occur at the interface between the two plates, at depths ranging from the earth's surface down to about 600 km. 2  This region, called the Benioff Zone , is used to locate the subducting plate, as shown for the case of Japan on the left-hand side of Figure 2. Second, in most subduction zones, there is an inland volcanic arc running parallel to the trench. 2  But in southern Mexico, the volcanic arc bends away from the trench, at about a 15Â° angle (see Figure 1). 3  Finally, in most subduction zones, giant earthquakes occur every few hundred years or so.