Find $y'$ by implicit differentiation. Match the equations defining $y$ implicitly with the letters labeling the expressions for $y'$.

1. $3 \sin (x-y) = 5 y \sin x$
2. $3 \cos (x-y) = 5 y \cos x$
3. $3 \cos (x-y) = 5 y \sin x$
4. $3 \sin (x-y) = 5 y \cos x$

A. $\displaystyle y' = \frac {3 \cos (x-y) - 5 y \cos x } {3 \cos (x-y) + 5 \sin x }$
B. $\displaystyle y' = \frac {3 \cos (x-y) + 5 y \sin x } {3 \cos (x-y) + 5 \cos x }$
C. $\displaystyle y' = \frac {-3 \sin (x-y) + 5 y \sin x } {5 \cos x - 3 \sin (x-y) }$
D. $\displaystyle y' = \frac {-3 \sin (x-y) - 5 y \cos x } {5 \sin x - 3 \sin (x-y) }$

In order to get credit for this problem all answers must be correct.