4. The Lotka-Volterra predator-prey model is used to model a biological system in which two species, one a predator and one a prey, interact with each other. If x is the number of prey animals and y is the number of predator animals, then one way of expressing the Lotka-Volterra model is through the implicit equation
\(V = \delta x - \gamma \ln(x) + \beta y - \alpha \ln(y)\)
where \(\alpha, \beta, \gamma, \delta\), and V are constants that depend on species and environmental factors. Determine the sensitivity of the predator population to changes in the prey population by computing the derivative \(\frac{dy}{dx}\). (Use implicit differentiation.)
