Answer:
dy/dx = ( 2x - y^2 - 1) / (3y^2 + 2xy + 1).
Step-by-step explanation:
Cross multiply:
x^2 = (x + y)(y^2 + 1)
Using the Chain and Product rules:
Finding the derivative:
2x = (x + y)(2y dy/dx) + (y^2 + 1)(1 + dy/dx)
2x = 2xy dy/dx + 2y^2 dy/dx + y^2 + y^2 dy/dx + 1 + dy/dx
2xy dy/dx + 2y^2 dy/dx + y^2 dy/dx + dy/dx = 2x - y^2 - 1
3y^2 dy/dx + 2xy dy/dx + dy/dx = 2x - y^2 - 1
dy/dx = ( 2x - y^2 - 1) / (3y^2 + 2xy + 1).
