What is the derivative of #lnx / x#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Guilherme N. Dec 24, 2015 Using quotient rule, which states that for #y=f(x)/g(x)#, #(dy)/(dx)=(f'(x)g(x)=f(x)g'(x))/g(x)^2# Explanation: Solving: #(dy)/(dx)=((1/x)x-lnx(1))/x^2# #(dy)/(dx)=(1-lnx)/x^2# 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 1333 views around the world You can reuse this answer Creative Commons License