Differential equations without derivation In my introductory physics book there is this equation:
$$U=\frac{PV}{(\gamma -1)}$$
that is transformed to
$$dU=\frac{Pdv+Vdp}{(\gamma -1)}$$
It seems like a derivative operation, but where are the differentials at the denominators?
What kind of operation is this? And under which conditions can be applied?
Thanks.

We starts with
$$U=\frac{PV}{(\gamma -1)}$$
I'll just differentiate this w.r.t a dummy variable $x$, assuming $\gamma$ is a constant.
$$\frac{dU}{dx}=\frac{P\frac{dV}{dx}+V\frac{dP}{dx}}{(\gamma -1)}$$
Multiplying $dx$ throughout,
$$dU=\frac{PdV+VdP}{(\gamma -1)}$$
as shown.
