Solving by using log will be slightly easy:
Taking log on both sides, you get,
(sin y)( log x) + (sin x)( log y)=0
Now differentiate wrt x,
you will get,
{(sin y)/x+(log x)(cos y)(dy/dx)} +( -cos x)/y(dy/dx)+(log y)(cos x)=0
Simplify this and u'll surely get the answer.