How do you find the second derivative of #y=ln((2x)/(x+3))# ? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer A. S. Adikesavan Nov 18, 2016 #1/(x+3)^2-1/x^2# Explanation: #y= ln 2 + ln x - ln (x|3)# #y'=0+1/x-1/(x+3)=x^(-1)-(x+2)^(-1)# #y''=(-1)x^(-1-1)-(-1)(x+2)^(-1-1)(x+3)'# #=-1/x^2+1/(x+3)^2(1)# 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 1113 views around the world You can reuse this answer Creative Commons License