But now let's think about what happens if we take the derivative of this function right over here. So what happens when we take the derivative of a position as a function of time? So remember, the derivative gives us the slope of the tangent line at any point. So let's say we're looking at a point right over there. The slope of the tangent line, it tells us for a very small change in t, I'm exaggerating it visually, for a very, very small change in t, how much are we changing in position? How much are we changing in position? So we write that as ds dt is the derivative of our position function at any given time.