What is the derivative of #y=ln(ln(x))#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Rhys Mar 20, 2018 #(dy)/(dx) = 1/(xlnx) # Explanation: #d/dx ln f(x) = ( f'(x) ) / f(x) # #=> d/dx( ln ( ln x ) ) = (d/dx( lnx )) /lnx# #= (1/x)/lnx # #1/( xlnx ) # 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 117013 views around the world You can reuse this answer Creative Commons License