How do I find the derivative of #ln(sqrt(x)) #? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer mason m Dec 20, 2015 #1/(2x)# Explanation: According to the chain rule, #d/dx[ln(u)]=(u')/u# Therefore, #d/dxln(x^(1/2))=(d/dx[x^(1/2)])/x^(1/2)=(1/2x^(-1/2))/x^(1/2)=1/(2x^(1/2)x^(1/2)# #=1/(2x)# 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 4947 views around the world You can reuse this answer Creative Commons License