How do I find the derivative of #(x) = log_6x#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Jim H Jan 20, 2017 #log_6 x = lnx/ln6# Explanation: #f(x) = log_6 x = lnx/ln6 = 1/ln6 * lnx#, so #f'(x) = 1/ln6 d/dx(lnx) = 1/ln6 * (1/x) = 1/(xln6)# 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 2023 views around the world You can reuse this answer Creative Commons License