From your other post, you might have been a bit tired due to sleep deprivation, ...

From your other post, you might have been a bit tired due to sleep deprivation, so don't be too hard on yourself for not getting it ;)

As for the expression, you just have to expand it:

  y+dy = (x+dx)^-2 
       = 1 / (x+dx)^2 
       = 1 / (x^2 + 2xdx + d^2x) 
       = 1 / [x^2 * (1 + 2dx/x + d^2x / x^2)] 
       = 1 / [x^2 * (1 + dx/x)^2]
       = [x^2 * (1 + dx/x)^2]^-1
       = x^-2 * (1 + dx/x)^-2

It looks like a bit of a jump at first, but he just skipped the expansion of the expression. When I see this kind of thing, it helps me to just mess around with both start and end to see if I can find a way to get from one to the other.