why is the derivative of a constant 0?

Answer 1

derivative is rate of change. a constant doesn't change.

Answer 2

Let y = C where C is a constant
Then for any incremnet in x, y does not change.
So delta y/delta x = 0
Therefore dy/dx = lim delta x --> 0 (delta y/delta x) = 0

You should beable to see this geometrically because the line y = C is a horizontal line with slope = 0. Since the derivative = slope then derivative of a constant must be 0.

Answer 3

The derivative of any constant is zero.