13.6     Directional Derivatives and Gradient        by SGLee - HSKim, YJLim, THKim

                                                                          http://youtu.be/2_7TOUuzJoE

1. Find the directional derivative of the function  at the point  

    in the direction of the vector .

     ,  =>  , 

               .

2. Find the directional derivative of the function  at the point 

    in the direction of the vector .

      =>  and .

     ,  =>  , 

               .

3. Find the directional derivative of the function  at the point 

    in the direction of the vector .

      .

 4. If , find .

           http://matrix.skku.ac.kr/cal-lab/cal-12-2-2.html

Therefore, .

5. Find the gradient of  at the point .

      .

6. Use the definition of the gradient, assume that  and  are differentiable function on ,

    and let  be a constant. Prove the following gradient rules.

   (1) 

   (2) 

   (3) 

   (4)  

  and  are differentiable function on 

     (1)

              .

        ex)

     (2)

                .

        ex)

     (3)

              .

        ex)

     (4) 

              .

        ex)

7. Find the gradient of .

      , 

               .

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