Final answer:
The question requires finding dy/dx for a given equation by using implicit differentiation, which is not explicitly related to the provided examples and equations from different contexts.
Step-by-step explanation:
The question asks to find the derivative of the function dy/dx by using implicit differentiation.
The given equation is x²/x + y = y² + 8. To begin, we must differentiate both sides of the equation with respect to x. However, the provided information does not seem relevant to the process of differentiation, and therefore the correct implicit differentiation procedure has to be applied to the equation in question.
This process involves differentiating each term with respect to x, applying the chain rule where necessary, and finally solving for dy/dx.