u are using dx in the sense of a second point of x, or a change in x
check out this page from wikiversity that breaks everything down really well.
normally i know that posts from wiki are frowned upon, but i learnt from this site and i think they break it down really rigorously and guide you nicely through the expansion of a function into a summed power series and then into taylors series at different points. http://en.wikiversity.org/wiki/Taylor's_series
Saying "Taylor Series" is not enough, you have to attach a point around which you are expanding the function. Notice that around a different point, the taylor series will also have different coefficients.
In your example, f(x+dx) was calculated around a point x, so of course substitution won't work for the exapnasion of f(x) around 0.