What is the derivative of #f(x)=log_2(cos(x))# ? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Martin C. Mar 18, 2018 #-tan(x)/ln(2)# Explanation: #f(x)=log_2(cos(x))=ln(cos(x))/ln(2)# #1/ln(2)# is just a constant and can be ignored. #(ln(u))'=(u')/u# #u=cos(x), u'=-sin(x)# #f'(x)=1/ln(2)*(-sin(x))/cos(x)=-tan(x)/ln(2)# Answer link Related questions What is the derivative of #f(x)=log_b(g(x))# ? What is the derivative of #f(x)=log(x^2+x)# ? What is the derivative of #f(x)=log_4(e^x+3)# ? What is the derivative of #f(x)=x*log_5(x)# ? What is the derivative of #f(x)=e^(4x)*log(1-x)# ? What is the derivative of #f(x)=log(x)/x# ? What is the derivative of #f(x)=log_11(tan(x))# ? What is the derivative of #f(x)=sqrt(1+log_3(x)# ? What is the derivative of #f(x)=(log_6(x))^2# ? What is the derivative of #f(x)=sin(log_2(x))# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question 11769 views around the world You can reuse this answer Creative Commons License