The Difference
It seems a peculiarly etiolated view of difference. Right in the opening page of Repetition & Difference Deleuze writes:
The subject dealt with here is manifestly in the air. The signs may be
noted: Heidegger's more and more pronounced orientation towards a
philosophy of ontological Difference; the structuralist project, based upon
a distribution of differential characters within a space of coexistence; the
contemporary novelist's art which revolves around difference and
repetition, not only in its most abstract reflections but also in its effective
techniques; the discovery in a variety of fields of a power peculiar to
repetition, a power which also inhabits the unconscious, language and art.
That is three notions of difference mentioned and none of which we relates even tangentially to the calculus! (By the way, it's most likely that the difference and repetition in the novel, refers to the Roman Nouveau of Robbe Grillet, a most singularly anti-novel form of novel). Deleuze relates this to:
All these signs may be attributed to a generalized anti-Hegelianism:
difference and repetition have taken the place of the identical and the
negative, of identity and contradiction. For difference implies the negative,
and allows itself to lead to contradiction, only to the extent that its
subordination to the identical is maintained.
I can't say that I agree wholly with Deleuze on this last point...
The primacy of identity, however conceived, defines the world of representation. But modern thought is born of the failure of representation, of the loss of identities, and
of the discovery of all the forces that act under the representation of the
identical. The modern world is one of simulacra. Man did not survive God,
nor did the identity of the subject survive that of substance. All identities
are only simulated, produced as an optical ‘effect’ by the more profound
game of difference and repetition.
Deleuze is showing himself here as a Nieztschean here: when he writes 'Man did not survive God' he means that the idea of Man did not survive the 'death' of the idea of God. And hence - so long as you accept the Nieschtean dictum (many do - and many don't - and many haven't even heard of it - a fact which he conceals) - then the idea of Man requires reconceptualising of all the old categories. Hence the repetition without real organic movement in thought (think of how the Higgs particle was named the God-particle when it has nothing to do with God in the old Christian/Islamic dispensation and hence is a name without real ontological import) - and hence simulcra. And notice how it is Schopenerian (the World as Representation) but solely as representation (the Will behind it is not mentioned) and hence again, simulcra.
Of course the most prominent anti-Hegel Hegelian is Marx, but he is no longer here to put him in conversation with Deleuze. However, a prominent Marxist has: Gaytri Spivak, who, in the beginning of Can the Sub-altern Speak? accuses Deleuze as 'systematically ignoring the question of ideology' through which 'a concealed Subject (the West) pretends that it has no geo-political determinations' and this whilst mounting 'a much publicised critique ... actually inaugurates a Subject ... while often providing a cover for this subject of knowledge.'
The Differential
I don't know who it is that you're quoting on Deleuze use of the differential but it's not correct. First, Deleuze, by rejecting Hegels ontology is forced to address only the phenomenal world, and this, as Aristotle already said over two millenia ago is characterised primarily as motion, and its this motion that can be characterised through the calculus which Deleuze is highlights with his eulogy to the differential - and boy, does he eulogies it:
Leibniz discovers in the clear, finite idea the restlessness of the infinitely small, a restlessness also made up of intoxication, giddiness, evanescence and even death.
Nevertheless, as his introduction already shows, it's a small part of Deleuze's overall project. In fact, he writes:
This procedure of the infinitely small, which maintains the distinction between essences (to the extent that oneplays the role of inessential to the other), is quite different to contradiction [highlighting again his anti-Hegelianism]. We should therefore give it a special name, that of 'vice-diction'.
Moreover, your highlighted text:
A derivative, dy/dx, determines the structure of a curve while nonetheless existing just outside the curve itself
mischaracterises the notion of tangency to a curve, the notion of a curve, and that of determination itself. Whilst tangency can in the usual smooth cases determine a curve. Its not at all necessary to determine a curve - a curve determines itself. Moreover, with less smooth curves, tangency need not even determine a curve. For example, the notion of tangency can be extended to Frechet spaces.
Then the differential equation [for a tangent to curve] need not have any solutions, and even if does, the solutions need not be unique.
This, if your mathematics is rusty, means that no curve may be determined, and even if it does, there may be more than one - the curves are at liberty. Even more, the tangent space is no more 'virtual' than the curve itself. It's as real as the curve and was first found discovered - not abstractly (virtually as your quoted author puts it) - but phenomenologically in the world. To think it exists virtually, over and above the curve (or under it!), is to show a paucity of ontological imagination.
