How do you differentiate f(x)=[2(ln x)]/sqrtx? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer mason m Nov 24, 2015 f'(x)=(2-lnx)/x^(3/2) Explanation: According to the Quotient Rule: f'(x)=(sqrtxd/dx[2lnx]-2lnxd/dx[sqrtx])/(sqrtx)^2 f'(x)=((2sqrtx)/x-lnx/sqrtx)/x f'(x)=((2x-xlnx)/(xsqrtx))/x f'(x)=((2-lnx)/sqrtx)/x f'(x)=(2-lnx)/x^(3/2) 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 1357 views around the world You can reuse this answer Creative Commons License