How do you differentiate #y=(x/e^x)Lnx#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Bdub Mar 31, 2017 see below Explanation: Use the Product Rule and the Quotient Rule #(fg)'=fg'+gf'# #(f/g)' = (gf'-fg')/g^2# #y=(x/e^x)lnx# #color(red)(f=x/e^x), color(blue)( g=lnx# #color(red)(f'=(e^x-xe^x)/e^(2x)), color(blue)( g'(x)=1/x# #color(green)(y'=fg'+gf'# #color(green)(y'=x/e^x*1/x+lnx*( e^x-xe^x)/e^(2x))# #color(green)(y'=cancelx/e^x*1/cancelx+lnx*( e^x-xe^x)/e^(2x))# #color(green)(y'=1/e^x+(lnx( e^x-xe^x))/e^(2x))# #color(green)(y'=(e^x+lnx( e^x-xe^x))/e^(2x))# Answer link Related questions What is the derivative of #f(x)=log_b(g(x))# ? What is the derivative of #f(x)=log(x^2+x)# ? What is the derivative of #f(x)=log_4(e^x+3)# ? What is the derivative of #f(x)=x*log_5(x)# ? What is the derivative of #f(x)=e^(4x)*log(1-x)# ? What is the derivative of #f(x)=log(x)/x# ? What is the derivative of #f(x)=log_2(cos(x))# ? What is the derivative of #f(x)=log_11(tan(x))# ? What is the derivative of #f(x)=sqrt(1+log_3(x)# ? What is the derivative of #f(x)=(log_6(x))^2# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question 1640 views around the world You can reuse this answer Creative Commons License