y = x -2

Because ( dy / dx ) = nxn-1, I understand that the derivative will be

( dy / dx ) = -2x

But my problem lies in how you get to that derivative.

Now I had expected the problem to be solved in the book in the following way:

y dy = ( x dx )-2

y dy = ( 1 / ( x2 2dx) (dx)2))

y dy = x-2 2x-1(dx) (dx)-2

y dy = x-2 2x-1(dx) - disregard (dx)-2

dy = 2x-1(dx) - remove the function

( dy / dx ) = 2x-1

But the Book solves it in a completely different way:

y dy = ( x dx )-2

y dy = x-2 ( 1 ( x / dx ))-2

It then proceeds to expand the equation by the binomial theorem, ending up with the same answer.

Why does Thompson do this? Why factor out x-2? Is it not easier to do it the first way rather than the second? I cant understand the logic behind this. He gives no reason for doing it in this way.