The application of hyperreal numbers and in particular the transfer principle to problems of analysis is called nonstandard analysis. One immediate application is the definition of the basic concepts of analysis such as the derivative and integral in a direct fashion, without passing via logical complications of multiple quantifiers. Thus, the derivative of f(x) becomes f ′ ( x ) = s t ( f ( x + Δ x ) − f ( x ) Δ x ) {\displaystyle f'(x)={\rm {st}}\left({\frac {f(x+\Delta x)-f(x)}{\Delta x}}\right)} for an infinitesimal Δ x {\displaystyle \Delta x} , where st(·) denotes the standard part function, which "rounds off" each finite hyperreal to the nearest real.