quotient rule formula for taking the derivative of a quotient with respect to y

Question

2y/(x^2+y^)

 

partial derivative of f with respect to y.

Answer 1

Assuming that f(x,y) = 2y / (x² + y²), 

 

    ∂f/∂y = [(x²+y²)(2) - 2y(2y)] / (x²+y²)²

 

             = (2x² - 2y²) / (x² + y²)²