How to calculate the order of an infinitesimal

[NBagley119]

I know how to find out if an infinitesimal delta is of the first order (if delta*y/delta*x=dy/dx+epsilon is approximately equal to (dy/dx)*delta*x, but how do you find out if an infinitesimal is of second order or higher and how do you find out what that order is?

Note: I will update this question with typesetting once I figure out how to use LaTeX.

 

[Eynstone]

The order of an 'infinitesimal' is always relative.

 

[NBagley119]

The order of an 'infinitesimal' is always relative.

Relative to what? And how do you find the order?

 

[NBagley119]

I know how to find out if an infinitesimal delta is of the first order (if $\frac{\delta y}{\delta x}$=$\frac{dy}{dx}$+$\epsilon\approx$$\frac{dy}{dx}$$\delta$x, but how do you find out if an infinitesimal is of second order or higher and how do you find out what that order is?