What is the derivative of 4pi and why?

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.