Hi! I'd be happy to help you find dy/dx using implicit differentiation for the given equation: 5x^2 + 7xy - y^2 = 3.
Step 1: Differentiate both sides of the equation with respect to x.
d(5x^2)/dx + d(7xy)/dx - d(y^2)/dx = d(3)/dx
Step 2: Apply the differentiation rules.
10x + (7x(dy/dx) + 7y) - 2y(dy/dx) = 0
Step 3: Solve for dy/dx.
(7x - 2y)(dy/dx) = -10x - 7y
(dy/dx) = (-10x - 7y) / (7x - 2y)
So, the derivative dy/dx is given by (-10x - 7y) / (7x - 2y).