We recall the {principle of general covariance| which allows us\ in general relativity\ to deduce laws of physics which hold in the presence of ravitation from laws which hold without ravitation\ and which is implemented by the {minimal prescription| "h mn \1 a #:"m n \9 a #[ Then\ we examine the formal prescription of scale!relativity theory from which we should be able to deduce laws which hold at quantum scales from laws which hold at classical scales[ This prescription requires us to replace\ in classical equations\ the total time derivatives d:dt by a {scale!covariant derivative| d:dt[ We show that such a prescription has actually to be extended[ Indeed\ it does not allow us to obtain a whole set of complex scale!covariant equations\ which yield\ in all cases\ the right corresponding quantum equations[ We exhibit many basic cases for which the substitution "h mn \ 1 a #:"m n \9 a # is e.cient in general relativity\ while the prescription d:dt:d:dt does not lead to the right equations in scale!relativity[ These cases concern the HamiltonΓJacobi equation\ the form of {energy| * more generally the quadratic invariants * and the electromagnetic case[ Indeed\ we _nd that the usual quadratic form of nonrelativistic and relativistic invariants does not hold in this framework and that a divergence term appears in addition to the quadratic term[ Moreover\ we _nd that a current term is present with the Lorentz force in the equations of motion with an electromagnetic _eld[ Finally\ we point out that the operator d:dt does not ful_l the Leibniz rule[ We show that this fact may be related to the canonical commutation relations in quantum mechanics[ Moreover\ we show how it would be possible to connect\ in a systematic way\ the use of this operator with many relations of quantum mechanics\ in particular\ those where di}erential relations appear to be given by the correspondence principle[ Finally\ we show that we can recover the usual form of many equations * especially the fun! damental Leibniz rule * by extending the above!mentioned prescription by introducing a symmetric product f ) d:dt[ Γ 0888 Elsevier Science Ltd[ All rights reserved