Find the Jacobian of the Transformation $$x = 6 \alpha \sin \beta , y = 5 \alpha \cos \beta$$

Find the Jacobian of the transformation. $$x = 6 \alpha \sin \beta , y = 5 \alpha \cos \beta$$

A) $\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - 30 \alpha$
B) $\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - 20 \alpha \sin \beta \cos \beta$
C) $\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = 9 \alpha$
D) $\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - \alpha$
E) $\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = 36 \alpha$

Correct Answer:

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