question_answer

If \[{{e}^{x}}\,\sin \,y-{{e}^{y}}\,\cos \,x=1,\] then \[\frac{dy}{dx}\] is equal to

A)  \[\frac{{{e}^{x}}\,\sin \,y+{{e}^{y}}\sin x}{{{e}^{y}}\cos \,x-{{e}^{x}}\cos \,y}\]

B)  \[\frac{{{e}^{x}}\,\sin \,y+{{e}^{y}}\sin \,y}{{{e}^{y}}\cos \,x-{{e}^{x}}\cos \,y}\]

C)  \[\frac{{{e}^{x}}\,\sin \,y-{{e}^{y}}\sin \,x}{{{e}^{y}}\cos \,x-{{e}^{x}}\cos \,y}\]

D)  None of these.