Question

Найти производную функции y=sqrt(x)/(1+sqrt(x))

Answer 1

$y=frac{sqrt{x}}{1+sqrt{x}};\y'=frac{sqrt{x}'(1+sqrt{x})-sqrt{x}(1+sqrt{x})'}{(1+sqrt{x})^2}=frac{frac{1}{2sqrt{x}} (1+sqrt{x})-sqrt{x}frac{1}{2sqrt{x}} }{1+2sqrt{x}+x}=\=frac{frac{1}{2sqrt{x}}+frac{1}{2}-frac{1}{2}}{1+2sqrt{x}+x}=frac{0,5x^{-0,5}}{1+2sqrt{x}+x}=frac{1}{2sqrt{x}+4x+2xsqrt{x}};$