Answer:
[tex]\frac{x+2}{2x^2+2x}[/tex]
Step-by-step explanation:
We are given: [tex]f(x)=\ln(\frac{x}{(x+1)^{1/2}} )[/tex]
We will use the Division and Logarithm properties of the Derivative.
[tex]f'(x)=\frac{\frac{\sqrt{x+1}-x\frac{1}{2\sqrt{x+1}} }{x+1} }{\frac{x}{\sqrt{x+1}} } =\frac{x+2}{2x^2+2x}[/tex]
