#"Apply the definition of |x| : "# #f(x) = |x| => # #{ ( f(x) = x, x >= 0 ), ( f(x) = -x, x<= 0 ) :}# #"Now derive : "# #{ ( f '(x) = 1, x >= 0), ( f '(x) = -1, x <= 0 ) :}# #"So we see there is a discontinuity in x=0 for f '(x)."# #"For the rest, it is differentiable everywhere."#