Exercise 5.  Let  ,  where  u  and  v  are differentiable.   Show that

        .  

Solution 5.

See text and/or instructor's solution manual.

Answer.   This follows from (6-8)   ,

and the fact that if  u  and  v  are differentiable, then  f  is differentiable,  and   .

Solution.   Given   ,   we have   .  

Now apply  (6-8)   .

Use the function    and observe that  

                       

Therefore,

                    .

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell