Verified answer

d/dx (cos(x/y))

Use the chain rule, d/dx(cos(x/y)) = ( dcos(u))/( du) ( du)/( dx),

where u = x/y and ( dcos(u))/( du) = -sin(u):

= sin(x/y) (- (d/dx(x/y)))

Factor out constants:

= sin(x/y) (- (d/dx(x))/y)

The derivative of x is 1:

= - (sin(x/y))/y