Hi.
I have to prove that this function is decreasing: f(x) = ln(x+1)/x (http://www.wolframalpha.com/input/?i=ln(x+1)/x) .
I calculated the derivative to find the functions monotony, but I can't tell if it's negative of positive. The denominator is positive, but what about the nominator ? Would making the second order derivative will help me somehow ?
\(\displaystyle f'(x)\, =\, \dfrac{d}{dx}\left(\dfrac{\log(x\, +\, 1)}{x}\right)\, =\, \dfrac{\dfrac{x}{x\, +\, 1}\, -\, \log(x\, +\, 1)}{x^2}\)
thanks.
I have to prove that this function is decreasing: f(x) = ln(x+1)/x (http://www.wolframalpha.com/input/?i=ln(x+1)/x) .
I calculated the derivative to find the functions monotony, but I can't tell if it's negative of positive. The denominator is positive, but what about the nominator ? Would making the second order derivative will help me somehow ?
\(\displaystyle f'(x)\, =\, \dfrac{d}{dx}\left(\dfrac{\log(x\, +\, 1)}{x}\right)\, =\, \dfrac{\dfrac{x}{x\, +\, 1}\, -\, \log(x\, +\, 1)}{x^2}\)
thanks.
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