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

[latex]y= \sqrt{ \frac{x}{x+1}}=( \frac{x}{x+1}})^{0.5}[/latex] [latex]y'=0.5*( \frac{x}{x+1}})^{-0.5}*\frac{x'*(x+1)-x(x+1)'}{(x+1)^{2}}=0.5*( \frac{x}{x+1})^{-0.5}*\frac{x+1-x}{(x+1)^{2}}=\frac{1}{2 \sqrt{\frac{x}{x+1}}*(x+1)^{2}}=\frac{ \sqrt{x+1}}{2 \sqrt{x}*(x+1)^{2}}=\frac{1}{2 \sqrt{x(x+1)}*(x+1)}=\frac{1}{2 \sqrt{x^{2}+x}*(x+1)}[/latex]