How do you differentiate y=4x^0.5-8lnx? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer michael Dec 7, 2017 d/dx[4x^0.5 -8lnx] = (2sqrt(x)-8)/(x) Explanation: d/dx[4x^0.5 -8lnx] = 2x^-0.5-8/x ; power rule and derivative of natural logarithm = 2/(sqrt(x))-8/x = (2sqrt(x))/(x)-8/x ; rationalize the denominator = (2sqrt(x)-8)/(x) ; simplify 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 1849 views around the world You can reuse this answer Creative Commons License