Mth301 assignment no. 2 Latest solutions

							Spring 2012
Mth301 assignment # 2

Question # 1

Find the directional derivative of            f ( x, y ) y 2 ln x at P(1,4) in the direction of
a 3i  3 j .



       f ( x, y ) y 2 ln x

                               1
       f x ( x, y ) y 2 .
                               x
       f x (1, 4)16



       f y ( x, y )2 y ln x
       f y (1, 4) 0


      &

       a 3i  3 j
       ^      a
       a
           || a ||
       ^        3     3
       a         i    j
                18    18

      Therefore

                                 3                    3 
       Du f (1, 4)  f x (1, 4)         f y (1, 4)     
                                 18                   18 
                             3             3 
       Du f (1, 4)  (16)           (0)         
                             18            18 
                        16
       Du f (1, 4)  
                           2