How are reaction rate laws derived? Let's take the reaction $2A + B \rightarrow C$, with the assumption that this is an elementary reaction. If I'm only given this information, how would I derive the following forward rate law from scratch?

$$ 
\frac{dC}{dt} = k[A]^2 [B]
$$

I tried to find an answer online but most sources jump straight to the above format for a rate law. I also understand that there are many experimental considerations which can affect what is actually observed (e.g. pseudo $0^{th}$rate law behavior) but I just want to know if there's a way to derive these rate laws given just the reaction. Thank you.
I am not a professional or anything close, but I think the answer to your question is simply that $C$ is jointly proportional to $A$ and $B$. The following link explains joint-proportion (https://www.mathwords.com/jk/joint_variation.htm). Just in case, the link gets broken in the future: