Finding domain of a function.

Question

Given the function f(x, y) = y ln (4-4x²+y²)

1. Express the domain of f as a set.
2. Find f_xy for any point (x, y) on its domain

Answer 1

1. 4 - 4x² + y² > 0; 4x² - y² < 4; x² - y²/4 < 1 This is internal part of hyperbola.
2. f_x = y/(4 - 4x² + y²)(- 8x) = (- 8xy)/(4 - 4x² + y²); f_xy = - 8x(4 - 4x² + y² - 2y²)/(4 - 4x² + y²)²

-8x(4 - 4x² - y²)/(4 - 4x² + y²)²