dz/dx = v/(2 * (u * v)^(1/2)) * 1/(x^2+y^2)^(1/2) * 1/(2 * (x^2+y^2)^(1/2)) * 2 * x +
+ u/(2 * (u * v)^(1/2)) * y^2 =
= 1/2 * (v/u)^(1/2) * x/(x^2+y^2) + 1/2 * (u/v)^(1/2) * y^2
dz/dy = v/(2 * (u * v)^(1/2)) * 1/(x^2+y^2)^(1/2) * 1/(2 * (x^2+y^2)^(1/2)) * 2 * y +
+ u/(2 * (uv)^(1/2)) * 2 * x * y =
= 1/2 * (v/u)^(1/2) * y/(x^2+y^2) + x * y * (u/v)^(1/2)