Answer
$y' = \dfrac{-(\pi x \sin{(\pi x)}+\cos{(\pi x)+1)}}{x^2}$
The zeros of $y'$ represent the points on the graph of the original function where the tangent lines are horizontal.
Work Step by Step
The function is given by the equation $y=\dfrac{\cos(\pi x)+1}{x}$
Using a computer algebra system, the derivative of the function is:
$y' = \dfrac{-(\pi x \sin{(\pi x)}+\cos{(\pi x)+1)}}{x^2}$
The red curve represents the graph of the function. The blue curve represents its derivative.
The zeros of $y'$ represent the points on the graph of the original function where the tangent lines are horizontal.
