Computational effort of a derivation

How great is the computational effort of a derivation ?

If I calculate e.g. f(x)=N*4N*2N , than the effort would scale with N^3 -but what is the effort for df(x)/dx ?

Indeed you are right -each N actually stands for a sum of gauss functions from 1 to N.

...it's actually the computational cost of a SCF-cycle (quantum chemistry;) I'm interested in...or the derivation thereof to be precise.