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