# Differential notation help

A question: is it possible (maybe handling differentials, I don't know) to have in the same formula these two expressions: $$\frac{dp}{dq}$$ and
$$\frac{dq}{dp}$$?

I think it is illogical. It would imply that at same time p is a function of q and q is a function of p. That seems nonsense to me. Am I allright?

Hurkyl
Staff Emeritus
One route to happiness is to have p be a function of q, and if the conditions of the inverse function theorem are satisfied, we can (locally) define a function $\hat{q}$ with the property that $\hat{q}(p(q)) = q$, and then we can say that $dq/dp$ really "means" $d\hat{q}/dp$.