Consider a bar of any arbitrary cross-section subjected to loads in axial direction only. The bar is subjected to distributed axial load q(x) along its length.
The governing differential equation can be written by considering equilibrum of a differential element of length dx.
The axial force at x is denoted by F.
The axial force at (x + dx) is (F + (@F/@x)*dx) - based on Taylor Series expansion.

@ - stands for partail derivative.

I would like to get some information about the last statement. How to derive the force at x + dx and how it is related to Taylor series.

Thanks