Video narration
What changes during one tiny step up a ramp, and how could you measure it? As you walk forward, the ramp distance changes a little, and your height changes too. The forward change is the input, called dx. The change in height is the output, called dy. Now imagine the ramp's steepness. Its slope tells you how much height changes for each unit of forward distance. That local rate is the derivative. For a very small movement, dy is approximately the derivative multiplied by dx. Here's the important flip: a differential is not a mysterious new kind of number. It is simply a name for a tiny change. The derivative is different: it tells how the two tiny changes are related. This works as a close estimate for tiny movements, not an exact rule for a long walk. So, what changes in one tiny step? The differential measures the tiny change; the derivative tells how much height changes for each tiny forward change.