Find a Potential for the Given Vector Field $$\vec { F } ( x , y , z ) = \left\langle \frac { 1 } { x } , \frac { 1 } { y } , \cot ( z ) \right\rangle$$

Multiple Choice

Find a potential for the given vector field: $$\vec { F } ( x , y , z ) = \left\langle \frac { 1 } { x } , \frac { 1 } { y } , \cot ( z ) \right\rangle$$

A) $f ( x , y , z ) = \ln ( x y \tan ( z ) )$
B) $f ( x , y , z ) = \ln ( x y \cos ( z ) )$
C) $f ( x , y , z ) = \ln ( x y \sin ( z ) )$
D) $f ( x , y , z ) = \ln ( x y \sec ( z ) )$