What is the derivative of #ln(cos^2(x))#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Jim H Oct 20, 2015 #f(x) = ln(cos^2x) = ln((cosx)^2) = 2ln(cosx)# Explanation: #f'(x) = 2 1/cosx (-sinx)# #" "# (Chain rule: #d/dx(lnu) = 1/u (du)/dx#) # = -2tanx# 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 24878 views around the world You can reuse this answer Creative Commons License