How do you differentiate #f(x)=xln(1/x)-lnx/x #? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Konstantinos Michailidis Jan 3, 2016 It is #f'(x)=ln(1/x)-1-(1-lnx)/x^2# Explanation: The derivative is #d(f(x))/dx=x'*ln(1/x)+x*ln(1/x)'-((lnx)'x-x'*lnx)/(x^2)=> d(f(x))/dx=ln(1/x)+x*((1/x)'/(1/x))-(1-lnx)/x^2=> d(f(x))/dx=ln(1/x)-1-(1-lnx)/x^2# Remember that #d(lnx)/dx=1/x# Answer link Related questions What is the derivative of #f(x)=ln(g(x))# ? What is the derivative of #f(x)=ln(x^2+x)# ? What is the derivative of #f(x)=ln(e^x+3)# ? What is the derivative of #f(x)=x*ln(x)# ? What is the derivative of #f(x)=e^(4x)*ln(1-x)# ? What is the derivative of #f(x)=ln(x)/x# ? What is the derivative of #f(x)=ln(cos(x))# ? What is the derivative of #f(x)=ln(tan(x))# ? What is the derivative of #f(x)=sqrt(1+ln(x)# ? What is the derivative of #f(x)=(ln(x))^2# ? See all questions in Differentiating Logarithmic Functions with Base e Impact of this question 2006 views around the world You can reuse this answer Creative Commons License