Suppose you have a cube of length $s$. The volume of that cube is $$V=s^3.$$ Now let's suppose the dimensions of that cube (and hence its volume) depend on time. We are wondering about the relationship between the growth of the length versus the growth of the volume.
Suppose $$s(t) =t.$$
Then $s'(t) =$ and $V'(t) =$ .
Next, suppose $$V(t) = t.$$ Then $s'(t) =$ and $V'(t) =$ .