Question #55c21

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Answer 1 · 2017-11-06T16:22:23

Look below

First, apply the quotient rule of #F(x)=ln(x)/(x-1)#

#(\frac{d}{dx}[ln(x)]times(x-1)-ln(x)times\frac{d}{dx}[x-1])/((x-1)^2)#

#\frac{d}{dx}[ln(x)] = 1/x#

#\frac{d}{dx}[x-1] = \frac{d}{dx}[x]+\frac{d}{dx}[-1]#

#\frac{\frac{1}{x}(x-1)-ln(x)times(1+0)}{(x-1)^2#

the one goes into the #ln(x)#

#\frac{\frac{x-1}{x}-ln(x)}{(x-1)^2}#