The equation is part of the proof of the derivative of a negative exponent in "Calculus Made Easy" by Silvanus P. Thompson.

The book says (x+dx)^-2 = x^-2(1+dx/x)^-2

I make it x^-2(1+2.dx/x)^-1

I know I am wrong but don't know how.

Note: (dx)^2/x^2 is dropped as it is infintesimal.