Chapter 14: Partial Derivatives - Section 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 7

$f_x=1/2(x^2+y^2)^{-1/2}\times 2x$ $f_y=1/2(x^2+y^2)^{-1/2}\times 2y$

Take the first partial derivatives of the given function. When taking a partial derivative with respect to x, treat y as a constant, and vice versa: $f_x=1/2(x^2+y^2)^{-1/2}\times 2x$ $f_y=1/2(x^2+y^2)^{-1/2}\times 2y$