How do I find the derivative of #ln sqrt((4x-5)/(3x+5))#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Eddie Aug 7, 2016 #= 35/2 * (1)/((4x-5)(3x+5 ))# Explanation: #d/dx ( ln sqrt((4x-5)/(3x+5)))# #= d/dx ( 1/2 ln ((4x-5)/(3x+5)))# #= 1/2 d/dx ( ln (4x-5) - ln(3x+5 ))# #= 1/2 ( 4/(4x-5) - 3/(3x+5 ))# #= 1/2 ( (12x + 20 -12 x+15)/((4x-5)(3x+5 )))# #= 35/2 * (1)/((4x-5)(3x+5 ))# 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 1876 views around the world You can reuse this answer Creative Commons License