I was going through a silly doubt, but aren't able to find its answer. If we say something is changing with time, what do we mean by that? Should we multiply the quantity with time or divide it? Like if I say that the velocity is changing with time, what should I calculate? acceleration or distance? Similarly in definite integral and differentiation. If I say that something is changing with time, should I take differentiation or do difinite integral in interval $t$ to $t+\Delta t$?