Find the Direction in Which the Maximum Rate of Change $f ( x , y ) = 2 \sin ( x y ) , ( 1,0 )$

Multiple Choice

Find the direction in which the maximum rate of change of f at the given point occurs. $f ( x , y ) = 2 \sin ( x y ) , ( 1,0 )$

A) $\langle2,0 \rangle$
B) $\langle1 , - \sqrt { 2 } \rangle$
C) $\langle \sqrt { 2 } , 0 \rangle$
D) $\langle0,2 \rangle$
E) $\left\langle\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right\rangle$