The curve in question is $$y = \frac{\ln(x)}{1+x}.$$ So differentiating with respect to $x$ in the equation, we get $$\frac{dy}{dx} = \frac{(1+x)\frac{1}{x} - \ln(x)}{(1+x)^2}$$. Which we can equate to zero and simplify the equation as:
$$(1+x)\frac{1}{x} - \ln(x) = 0.$$ How do I even solve this in order to find the x coordinate of the stationary point? I checked with a graphic calculator that there is indeed a stationary point for this.