If f(x)=x3 Sgn, then

Note.x3Sgn x=x3,      if x>00,         if x=0−x3,  if x<0Clearly f is continuous at x=0f'0−=ddx−x3x=0=0f'0+=ddxx3x=0=0∴f'(0)=0⇒f is derivable at x=0.