Derivatives

In the car today...

E: Daddy!  The derivative is negative!
M: Indeed, the car is going down hill...
E: Daddy! For the cars going the other way, the derivative is positive!
M: Yes, Edwin...
E: What if the car goes backwards?
M: Well, the the derivative will be positive. The derivative with respect to time will be positive.  The derivative with respect to position will stay negative.
E: (giggles)

...

E: (giggling) Daddy! What is the derivative of time? (more giggles)
M: With respect to what? Time?
E: Yes!
M: That would be 1.
E: What if it was derivative of time respect to a clock?
M: If the clock was working correctly it would be 1
E: What if the clock was running backwards? (giggles) Would it be negative? Then the clock would ring at the wrong time!