What is the first differential of #f(x) = 1/(x(1+lnx)# ?

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Answer 1 · 2017-03-03T06:01:25

#-(2+lnx)/(x^2(1+lnx)^2#

#f(x) = 1/(x(1+lnx)#

#= (x*(1+lnx))^-1#

Applying the power rule and the chain rule:

#= -(x*(1+lnx))^-2 * d/dx(x*(1+lnx))#

#= -(x*(1+lnx))^-2 * x*(0+1/x)+(1+lnx)*1#
[Product rule and standard differential]

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

#= -(2+lnx)/(x^2(1+lnx)^2#