How do you differentiate #y=lnx/x^20#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Bdub Oct 31, 2016 #dy/dx=(x^19-20x^19 ln x)/x^40# Explanation: #y=lnx/x^20# Use quotient rule #(f/g)^' = (gf'-fg')/g^2# #f=ln x, g= x^20# #f'=1/x, g'=20x^19# #dy/dx=(gf'-fg')/g^2# #dy/dx=(x^20*1/x-lnx *20x^19)/(x^20)^2# #dy/dx=(x^19-20x^19 ln x)/x^40# 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 1563 views around the world You can reuse this answer Creative Commons License