That's actually an interesting issue in control systems. IIRC, if you set up a system so that some variable B is a function of the time-derivative of A, B=f( dA(t)/dt ), and it requires you to know dA(T)/dt to compute B(T), such a system is called "acausal". I believe this is because you can't know dA(T)/dt until you know A(t) after time T.

So any physically-realizable system that depends on the time-derivative of some other value, is actually depending on the time-derivative at a previous point in time.

In contrast, there is no such problem for the integral. If I only know the time series of A(t) up to time T, then I know the integral of A up to time T, and such a relationship is not acausal.

In the general case, for a relationship between two systems where B is a function of A, the transfer function from A to B, num(s)/den(s) must be such that the deg(num) <= deg(den), where deg() denotes the degree of a polynomial.

(The transfer function is ratio of B to A in the Laplace domain, usually given the variable s to replace t. Multiplying by s in the Laplace domain corresponds to differentiation in the time domain, and dividing by s is integration.)

(edit to clarify, then again to clarify some more)