Find the Jacobian $\frac { \partial ( x , y ) } { \partial ( u , v ) } \text { for the following change of variables: }$

Multiple Choice

Find the Jacobian $\frac { \partial ( x , y ) } { \partial ( u , v ) } \text { for the following change of variables: }$ $x = \frac { 1 } { 4 } ( 9 u - 4 v ) , y = \frac { 1 } { 4 } ( 3 u + 3 v )$

A) $\frac { 27 } { 16 }$
B) $- \frac { 45 } { 4 }$
C) $- \frac { 27 } { 16 }$
D) $\frac { 39 } { 16 }$
E) $- \frac { 39 } { 16 }$