What is the derivative of #lnx/x^2#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer sjc Dec 3, 2016 #f'(x)=(1-lnx^2)/x^3# Explanation: use the quotient rule, which should be memorised. #f(x)=u/v" "=>" "f'(x)=(vu'-uv')/v^2# #f(x)=(lnx)/x^2# #u=lnx=>u'=1/x# #v=x^2=>v'=2x# #f'(x)=(x^2xx1/x-2xlnx)/(x^2)^2# #f'(x)=(x-2xlnx)/x^4=(x(1-2lnx))/x^4=(cancel(x)(1-lnx^2))/(cancel(x^4)x^3)# 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 8078 views around the world You can reuse this answer Creative Commons License