Compute the Gradient of the Function at the Given Point $$f ( x , y ) = \tan ^ { - 1 } \frac { - 9 x } { y }$$

Multiple Choice

Compute the gradient of the function at the given point.
- $$f ( x , y ) = \tan ^ { - 1 } \frac { - 9 x } { y }$$

A) ${\nabla} f = - \frac { 3 } { 37 } \mathrm { i } + \frac { 2 } { 37 } \mathrm { j }$
B) ${\nabla} f = - \frac { 3 } { 38 } \mathbf { i } + \frac { 1 } { 19 } \mathbf { j }$
C) ${\nabla} f = - \frac { 3 } { 38 } \mathrm { i } - \frac { 1 } { 19 } \mathrm { j }$
D) ${\nabla} f = - \frac { 3 } { 37 } \mathrm { i } - \frac { 2 } { 37 } \mathrm { j }$