Answer
$y' = \dfrac{1}{\sqrt{2}(x+1)^2 \sqrt{\dfrac{x}{x+1}}}$
The derivative of the function has no zeros.
Work Step by Step
The function is given by the equation $y=\sqrt{\dfrac{2x}{x+1}}$
Using a computer algebra system, the derivative of the function is:
$y' = \dfrac{1}{\sqrt{2}(x+1)^2 \sqrt{\dfrac{x}{x+1}}}$
The function is represented by the red curve and its derivative by the blue curve.
The derivative of the function has no zeros.
