Let f(x, y) = (x^2 - y^2) / (x^2 + y^2). Find the partial derivatives of f(x, y) with respect to x and y.

: Orthogonal systems, trigonometric series, and the calculation of Fourier coefficients.

To find the limit of f(x, y) as (x, y) approaches (0, 0), we can use the definition of a limit. Let ε > 0 be given. We need to find a δ > 0 such that |f(x, y) - 0| < ε whenever 0 < √x^2 + y^2 < δ.