In each scenario, find \(\frac{dy}{dx}\).
1. $$xy = x + 2$$
2. $$y^3 = x^2 - 5$$
3. $$y^2 + y = 5x$$
4. $$xy^2 - 5x = 3$$
5. $$x^2y^2 + xy + 4 = x$$
6-10. In Problems 1-5, find the second derivative of \(y\) in terms of \(x\).
11a. Find the slope of the tangent line on
$$xy = 5x + 3$$ when \(x = 1\) and when \(x = 2\).
b. Find \(\frac{d^2y}{dx^2}\).