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