A curve has the equation: x^2(4+y) - 2y^2 = 0 Find an expression for dy/dx in terms of x and y.

First of all expand the brackets in the equation. Then you can differentiate each term with respect to x. As one of the terms will be a product of x and y the product rule must be used to find the differential of that term. The key to these types of questions is that the differential of y with respect to x is dy/dx. This means that after differentiating each of the terms you will have an expression in terms of dy/dx, x and y. All you have to do from that point on wards is gather the terms with the dy/dx on one side to find an expression for dy/dx.After expanding the brackets:4x² + x²y - 2y² = 0After differentiating each term:8x + 2xy + x²(dy/dx) - 4y(dy/dx) = 0After rearranging to make (dy/dx) the subject:dy/dx = (8x+2xy)/(4y-x²)