How do you differentiate y=4x^0.5-8lnxy=4x0.5−8lnx? 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)ddx[4x0.5−8lnx]=2√x−8x Explanation: d/dx[4x^0.5 -8lnx]ddx[4x0.5−8lnx] = 2x^-0.5-8/x=2x−0.5−8x ; power rule and derivative of natural logarithm = 2/(sqrt(x))-8/x=2√x−8x = (2sqrt(x))/(x)-8/x=2√xx−8x ; rationalize the denominator = (2sqrt(x)-8)/(x)=2√x−8x ; simplify Answer link Related questions What is the derivative of f(x)=ln(g(x))f(x)=ln(g(x)) ? What is the derivative of f(x)=ln(x^2+x)f(x)=ln(x2+x) ? What is the derivative of f(x)=ln(e^x+3)f(x)=ln(ex+3) ? What is the derivative of f(x)=x*ln(x)f(x)=x⋅ln(x) ? What is the derivative of f(x)=e^(4x)*ln(1-x)f(x)=e4x⋅ln(1−x) ? What is the derivative of f(x)=ln(x)/xf(x)=ln(x)x ? What is the derivative of f(x)=ln(cos(x))f(x)=ln(cos(x)) ? What is the derivative of f(x)=ln(tan(x))f(x)=ln(tan(x)) ? What is the derivative of f(x)=sqrt(1+ln(x)f(x)=√1+ln(x) ? What is the derivative of f(x)=(ln(x))^2f(x)=(ln(x))2 ? See all questions in Differentiating Logarithmic Functions with Base e Impact of this question 1850 views around the world You can reuse this answer Creative Commons License