I am a physics novice (no formal science education beyond age 16) reading "Space Time and Quanta" by Robert Mills. At one point in the book whislt demonstrating the derivation of 1/2 mv^2 he says "mv dv = 1/2m d(v^2) = d(1/2mv^2)". I have been looking at this for quite a while and consulted other books on calculus but am unable to follow these steps. He seems to be using the reverse power rule to do something similar to integrating it. Could someone please explain these steps to me?