I need to compute the derivate of
$g(x) = \ln\left(\frac{1}{x \sqrt{x+1}}\right)$
Simplifying this I get
$g(x) = \ln(1) - (\ln x + \frac{1}{2}\ln(x+1))$
Evaluating the derivate I get
$g'(x) = 0-(\frac{1}{x} + \frac{1}{2x+2})$
I have compared my result to WolframAlphas answer and while my denominator is the same my numerator is different. My result is $-3x+2$ WA result is $-x+2$.
I assume my mistake is in the multiplication of the negative sign, but why is this wrong?
Thank you