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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

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Looks OK. Presumably you fed the simplifed version of $g(x)$ into Wolfram Alpha, without parentheses. Wrong input, wrong output. – André Nicolas Aug 12 '12 at 7:16
I input the following into WA. "derivative of ln(1/x*sqrt(x+1))" And so yes, it seems I input the wrong equation into WA. Thank you – Michael Frey Aug 12 '12 at 7:23
up vote 1 down vote accepted

Wolfram Alpha says the same thing. Take a common denominator and check for yourself, your derivative is fine. I just checked and got -(3x+2) from WA.

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I see. My error was that i forgot the additional parenthesis when inputting the equation in WA. – Michael Frey Aug 12 '12 at 7:26

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