Let and be differentiable at Let and
               
be functions such that
             
If x, y are both differentiable at then the composite function
             given by
             is differentiable at
and
            
Functionally, this is also written as

            

Let
          
Then, by differentiability of , we have for ,
          
Thus for
          
                                              --------(28)
Since are continuous, as Hence, as , it follows from (28) that is differentiable and