Optimimality condition for quantile estimators


I'm trying to understand a passage in Koenker's Quantile regression book (p.33).
It says: (note that y,x, are vectors and w is the direction vector)

With the first part of the outcome no problem: I apply the product rule for derivatives and the derivative of the indicator function is 0 since the discontinuity of the indicator function doesnt happen in y-x'b different from zero. But what happens in y-x'b=0? My logical mind tells me that there is no derivative for the indicator function if not some complex approximation, so how came Koenker up with that result?