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 ?

liek dis?

E = \sum_{\mu \nu} P_{\mu \nu} h_{\mu \nu} + 0.5 \sum_{\mu \nu \kappa \lambda} P_{\mu \nu} P_{\kappa \lambda} (\chi_\mu \chi_\nu "|" \chi_\kappa \chi_\lambda )

There really needs to be a post preview thingee here.