Why is derivative of constant zero?

Use the limit definition of the derivative:

##f'(x)=lim_(hrarr0)(f(x+h)-f(x))/h##

If ##f(x)="C"##, where ##"C"## is any constant, then

##f(x+h)="C"##

Thus,

##f'(x)=lim_(hrarr0)("C"-"C")/h=lim_(hrarr0)0/h=lim_(hrarr0)0=0##