http://en.wikipedia.org/wiki/Marginalism: is marginalism overall a form of ideological sophistry? You tell me. Read the Wikipedian boilerplate here and ask yourself if it makes any real sense. It may, but the sudden appearance of a partial derivative to express marginal utility is the point at which the dog starts to bark. Who goes there?
In general the application of calculus suggests a coherent dynamical analysis of an ‘economy’, but I can never seem to find one when I examine textbooks here. I simply don’t see how calculus methods can be applied to the abstractions such as utility. Calculus was a subject devised to explain physical situations. Their application to economic abstraction has no foundational defense that I know of. It is always possible to find applications of derivatives, e.g. population growth, etc, and the one or two cases where this happens in economics are misleading.
I think that the use of calculus is misleading. Calculus was devised for physical bodies, and even such a simple parallel case of electromagnetism shows the whole of calculus reinvented via vector analysis, and then again for quantum mechanics, and then again for general relativity. But with economics we have the original calculus passed over into an exotic and very different subject matter. And the results are rarely subject to calculations, they are merely window dressing expressing a sort of ‘in principle’ case.
I think the whole question of what is an economic theory needs to be recast. That is already present in the various computerized models that actual data. And any number of other mathematical finesses in the field’s subject matter. This situation is so confused that we think we are dealing with a science, but the reality is different.