What is the derivative of #(ln x) ^ cos x#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer bp Jun 27, 2015 #(lnx)^cosx ( -sinx ln lnx + cosx /(x lnx))# Explanation: Let #y=(ln x)^cos x#, so that ln y= cos x ln ln x Now differentiate both sides, #1/y dy/dx = -sinx ln ln x + cos x 1/lnx 1/x# #dy/dx= (lnx)^cosx ( -sinx ln lnx + cosx /(x lnx))# 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 4350 views around the world You can reuse this answer Creative Commons License