What is the derivative of 4pi and why?

Answer: The derivative of 4pi (4π) is simply zero. In Calculus, the process of differentiation is taking the limit of the given as the change with respect to a certain variable approaches zero. The derivative indicates the slope of a given function, the rate of change with respect to small increments to a reference axis or variable. As our given, 4π, is simply a constant, it does not change with respect to any infinitesimal increment to any variable; thus its derivative is zero.