Solve the Problem $f ( x , y ) = \tan ^ { - 1 } x y$

Multiple Choice

Solve the problem.
-About how much will $f ( x , y ) = \tan ^ { - 1 } x y$ change if the point $( x , y , z )$ moves from $\left( 9 \sqrt { 2 } , \frac { - 6 } { \sqrt { 2 } } \right)$ a distance of $\mathrm { ds } = \frac { 1 } { 10 }$ unit in the direction of $\mathbf { i } + \mathbf { j } ?$

A) $\frac { 3 } { 14585 }$
B) $\frac { 3 } { 5834 }$
C) $\frac { 21 } { 58340 }$
D) $\frac { 3 } { 58340 }$