In Maple, the signum function is defined as signum(x) = |x|/x, which is valid for real numbers but not for complex values. For complex numbers, a more accurate representation is x/|x|, applicable except at zero. The derivative of the signum function, expressed as d/dx {|x|/x}, results in signum(1,x), which is zero for nonzero real x and undefined at zero. The function signum(1,x,0) and signum(0,x,0) highlight the optional third argument in Maple, which allows users to specify the value of signum at zero, reflecting different conventions that either assign it a value of 0 or 1. For further details, users can refer to the help page by typing ?signum in Maple.