Let $$f(x) = \frac{x}{x^2 + 1}.$$ Find all the values of $x$ for which $f'(x) = 0$. What is the product of all these values?
(For example, if $f'(x)$ was equal to zero at the points 1, 2, and 3, then the answer would be 1*2*3 = 6.)

Product =