I am familiar with the standard rule of mixed partial derivatives in that the order in which you partially differentiate dosn't matter. I have just been considering whether the same rule applies if we take f(q,t) say where q=q(t) and we differentiate normally w.r.t t then partially w.r.t q. Is the order of these operations always immaterial in this case too? I can't find a counterexample but I havn't yet got a satisfactory insight into this problem. Anyone want to enlighten me?