Recently, I've been learning about rates and have found the concept fairly easy to understand in the case of a reaction with a single reactant, which is essentially solving $$f'(t) = kf(t)^n$$ where $f(t)$ gives the concentration of the reactant at time $t$. Now, for a reaction with two reactants, I'm not exactly sure how to represent the rate in terms of a function. My best guess was defining a function $r(t) = \left(x(t), y(t) \right)$ where $x(t)$ and $y(t)$ represent the concentration of both reactants respectively at time $t$, then solving $$\mid \nabla r(t) \mid=kx(t)^ay(t)^b $$ This boils down to mostly a math problem but I don't know much about multivariable calculus. I'd appreciate if anyone could provide an answer or a link to a source. Thanks.