How do you find the derivative of #ln(ln(3x))#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Wataru Apr 10, 2017 #[ln(ln(3x))]'=1/(x ln(3x))# Explanation: By applying Log Rule and Chain Rule repeatedly, #[ln(ln(3x))]'=1/ln(3x)cdot[ln(3x)]'# #=1/(ln(3x))cdot1/(3x)cdot(3x)'# #=1/(ln(3x))cdot1/(cancel(3)x)cdot cancel(3)# #=1/(xln(3x))# 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 7855 views around the world You can reuse this answer Creative Commons License