What is the derivatie of ln (x) / (1 - ln(x))?

My solution with the quotient rule:
(maybe there is more simple way, without the quotiënt rule?)
#1/(x(1-lnx)^2)#

The books answer:

#1/(x(ln x -1)^2)#

1 Answer
Apr 17, 2018

See below...

Explanation:

Your answer is correct!

#(1 - lnx )^2 = [ -( lnx - 1 ) ]^2 #

#= (-1)^2 * ( lnx - 1 )^2 #

#= (lnx -1)^2 #

#=> (1-lnx)^2 -= (lnx -1 )^2 #

Hence both answers are equivalent

Or try expanding, gives same result!