What is the derivative of #log_5sqrt(x^2-1)#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer A. S. Adikesavan Aug 8, 2016 #x/((ln 5)(x^2-1))# Explanation: #(log_5sqrt(x^2-1))'# #=(1/2)log_5(x^2-1))'# #=(1/2)((ln(x^2-1)')/ln 5)# #=(1/(2 ln 5))((2x)/(x^2-1))# #=x/((ln 5)(x^2-1))# 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_2(cos(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# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question 2654 views around the world You can reuse this answer Creative Commons License