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.
There are 3 types of plate boundaries-convergent, divergent, and transform. Convergent boundaries occur when 2 plates collide with each other and push each other. Neither plate will give way, so the crust on the plates rise up and form mountains and mountain ranges. Divergent boundaries form rift valleys, volcanoes, and deep-ocean trenches, and transform boundaries cause earthquakes. Plates slide, collide and shift.