Imagine you have a function $$f(A,B) =A \cdot B$$ where $A=g(t)$ and $B=h(t)$ and $g$ and $h$ are unknown.
You measure $f(A,B)$ at $t_0$ and $t_1$ and you see a difference (either positive or negative). This implies there was a variation in $A$ and/or $B$ during instants $t_0$ and $t_1$.
How do you compute the “importance” of each of $A$, $B$ variations with regards to the variation of $f(A,B)$?
Example 1: maybe $A$ relatively varied a lot between $t_0$ and $t_1$, but $B$ remained stable and $f(A,B)$ didn’t varied that much (e.g., the equation is much more sensible to variations in $B$ than in $A$).
Example 2: both $A$ and $B$ varied a bit, but a minor variation in $A$ would cause a bigger variation in $f(A,B)$.
Bonus questions: what if were there several polynomial terms in the equation (e.g., $f = A_1 \cdot B_1 +A_2 \cdot B_2 +A_3 \cdot B_3$)?
