How do you find the second derivative of #ln(x/2)# ? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Ratnaker Mehta Jul 6, 2016 #:. (d^2y)/dx^2=-1/x^2# Explanation: Let #y=ln(x/2)# We have to find #(d^2y)/dx^2.# We start with #y=ln(x/2)# and use Rules of Logarithmic Fun. to see that, #y=lnx-ln2# #:. (dy)/dx=1/x=x^-1.# #:. (d^2y)/dx^2=d/dx{dy/dx}....[Defn.] = d/dx(x^-1)=-1*x^(-1-1).# #:. (d^2y)/dx^2=-1/x^2.# 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 1373 views around the world You can reuse this answer Creative Commons License