y = x^(1/2) - arctg x^(1/2)
Тогда
y' = (x^(1/2) - arctg x^(1/2))' = 1/2 * x^(-1/2) - 1/(1 + x) * (x^(1/2))' =
= 1/2 * x^(-1/2) - 1/(1 + x) * 1/2 * x^(-1/2) = 1/2 * x^(-1/2) * (1 - 1/(1 + x)) =
= 1/2 * x^(-1/2) * x/(1 + x) = x^(1/2)/(2 + 2x)