For the reaction $3\mathrm{A}+2\mathrm{B}\to \mathrm{C}+\mathrm{D}$, the differential rate law can be written as

By definition, the differential rate law is the rate of change of concentration of the reactant or product divided by the corresponding stoichiometric number appeared in the balanced chemical equation. For a reactant, it carries negative sign as its concentration decreases with time.

For the reaction, 3A+2B→C+D, the differential rate law can be written as

$-\frac{1}{3}\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{C}\right]}{\mathrm{dt}}=\mathrm{k}\left[\mathrm{A}{]}^{\mathrm{n}}\right[\mathrm{B}{]}^{\mathrm{m}}$ as:

Rate, $\mathrm{r}=-\frac{1}{3}\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}=-\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{B}\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{C}\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{D}\right]}{\mathrm{dt}}=\mathrm{k}\left[\mathrm{A}{]}^{\mathrm{n}}\right[\mathrm{B}{]}^{\mathrm{m}}$.