How do you find the second derivative of # ln(x^2+4)# ? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Douglas K. Oct 15, 2016 #(d^2ln(x^2 + 4))/dx^2 = (8 - 2x^2)/(x^2 + 4)^2# Explanation: The chain rule is: #(d{f(u(x))})/dx = (df(u))/(du)((du)/dx)# Let #u(x) = x^2 + 4#, then #(df(u))/(du) =(dln(u))/(du) = 1/u# and #(du)/dx = 2x# #(dln(x^2 + 4))/dx = (2x)/(x^2 + 4)# #(d^2ln(x^2 + 4))/dx^2 = (d((2x)/(x^2 + 4)))/dx# #(d((2x)/(x^2 + 4)))/dx =# #{2(x^2 + 4) - 2x(2x)}/(x^2 + 4)^2 = # #(8 - 2x^2)/(x^2 + 4)^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 3296 views around the world You can reuse this answer Creative Commons License