When is the derivative zero ?
The absolute value function " u " : [ −1 , 1 ] → [ 0 , 1 ] , " u " ( " t " ) = | " t " | , which is not differentiable at " t " = 0 , has a weak derivative " v " known as the sign function given by formula_24 This is not the only weak derivative for " u " : any " w " that is equal to " v " almost everywhere is also a weak derivative for " u " .