The Temperature at the Point $( x , y ) \text { on a metal plate is } T = \frac { 9 x } { x ^ { 2 } + y ^ { 2 } } \text {. Find the }$

The temperature at the point $( x , y ) \text { on a metal plate is } T = \frac { 9 x } { x ^ { 2 } + y ^ { 2 } } \text {. Find the }$ direction of greatest increase in heat from the point $( 7,9 )$ . Round all numerical values in your answer to three decimal places.

A) $0.101 \hat { \mathbf { i } } - 0.023 \hat { \mathbf { j } }$
B) $0.034 \hat { \mathbf { i } } - 0.017 \hat { \mathbf { j } }$
C) $0.023 \hat { \mathbf { i } } - 0.034 \hat { \mathbf { j } }$
D) $0.038 \hat { \mathbf { i } } - 0.101 \hat { \mathbf { j } }$
E) $0.017 \hat { \mathbf { i } } - 0.067 \hat { \mathbf { j } }$