Найти производную сложной функции Y=log2 √x/x+1

$f'(x)=\dfrac{1}{\ln\left(2\right)}\cdot \left(\ln\left(\frac{\sqrt{x}}{x+1}\right)\right)'=\dfrac{1}{\ln\left(2\right)}\cdot \dfrac{x+1}{\sqrt{x}}\cdot \left(\dfrac{\sqrt{x}}{x+1}\right)'=$

$=\dfrac{x+1}{\ln\left(2\right)\,\sqrt{x}}\cdot \frac{\left(\sqrt{x}\right)'\cdot \left(x+1\right)-\left(x+1\right)'\cdot \sqrt{x}}{\left({x+1}\right)^{2}}=\dfrac{1}{2\,\ln\left(2\right)\,x}-\dfrac{1}{\ln\left(2\right)\,\left(x+1\right)}$