Change in $f(x,y,z) = xyz$

Question

Given the function $f(x,y,z) = xyz$, and two points $A:(a_1,a_2,a_3)$ and $B:(b_1,b_2,b_3)$. The change in $f$ from moving from one point to another is simply given by $\delta = f(b_1,b_2,b_3)-f(a_1,a_2,a_3)$, how can I apportion out $\delta$ to the change in each of the parameters? Basically I need to be able to say that the change in $x$ caused p% of $\delta$, the change in $y$ caused q% of $\delta$ and so on.