How do you find the derivatives of #y=(lnx)^3#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Roberto G. Feb 18, 2017 #dy/dx = 3((ln(x))^2/x)# Explanation: We can apply Chain Rule of Differentiation. #d/dx f@g(x)= [d/dx f(u)][d/dx u]# or #[f@g(x)]' = {f'[g(x)]}{g'(x)}# #Let# #u = lnx # and #f(x) = (...)^3# #d/dx f@g(x) =[3(lnx)^2][d/dx lnx] # #d/dx f@g(x) =[3(lnx)^2][1/x]# #d/dx f@g(x) = 3((lnx)^2/x)# 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 1977 views around the world You can reuse this answer Creative Commons License