f(x)/g(x) = f'(x) g(x) - f(x) g'(x) / g(x)^2

How do I find the derivative of something like cos(x) / sin(1/x) ?

= ( - sin x) sin(1/x) - cos (x) cos ( 1/x) / ( sin( 1/x )^ 2

I know this is not completely correct. What is the derivative of sin ( 1/x )? Do I leave the value as 1/x ?