What is the derivative of #lnsqrt(x^2+1)#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Antoine Apr 2, 2015 let #y = lnsqrt(x^2 + 1)# #=> y = ln(x^2 + 1)^(1/2) = 1/2ln(x^2 + 1)# # (dy)/(dx) = 1/2(2x xx1/(x^2 + 1)) = x/(x^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 1936 views around the world You can reuse this answer Creative Commons License