The signum function is the derivative of the absolute value function, up to (but not including) the indeterminacy at zero. More formally, in integration theory it is a weak derivative, and in convex function theory the subdifferential of the absolute value at 0 is the interval , "filling in" the sign function (the subdifferential of the absolute value is not single-valued at 0). Note, the resultant power of is 0, similar to the ordinary derivative of . The numbers cancel and all we are left with is the sign of .