In mathematical parlance, we say "take the derivative of a function f" to indicate that we are computing a new function, which maps slopes, that derives from f. However, in physics, we say "take the derivative of velocity". However, velocity is a quantity, not a function. What does it mean to take a derivative of a quantity? This goes for mathematics in general. If we have y = f(x), y is a quantity, not a function that maps between two sets. So what does it mean to "take the derivative of y"?