(ii) Let . Then is also differentiable for every . It is easy to show that

                                        
(iii) Let

     Then is differentiable at every with

                                      

      For does not exist. In fact, is not even continuous at .

        Click here to see a visualization(Java) : Applet 8.3

      The product rule for differentiation: for differentiable functions and ,
                                                   
       can be extended to higher derivatives as follows.