Final answer:
The integral expression given seems to be part of a larger context, likely involving a surface or line integral from vector calculus, where typically parameterization and then integration of the path or surface are performed.
Step-by-step explanation:
When faced with an integral of the form (g(x)f(y)dx/dy), none of the options listed (product rule, chain rule, or integration by parts) are directly applicable in a traditional sense. This is because the given expression appears to involve a partial differential and seems to be part of a larger context, likely from a surface integral or line integral from vector calculus. In vector calculus, when you have functions that need to be integrated over a certain path or surface, you typically parameterize the path or surface and then integrate accordingly. If the integrals involve multiple variables, they could be double integrals or even triple integrals depending on the dimensionality of the problem. To solve these, you need to express one variable in terms of the other one as suggested in the provided examples, such as expressing x in terms of y, or vice versa, and then carry out the definite integral over the given bounds.