How do you differentiate #y=lnx(x^5+10x^2-19)#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Shwetank Mauria Aug 7, 2016 #(dy)/(dx)=1/x(x^5+10x^2-19)+5x(x^3+4)lnx# Explanation: Using product rule, if #y=lnx(x^5+10x^2-19)# #(dy)/(dx)=1/x(x^5+10x^2-19)+lnx(5x^4+20x)# = #1/x(x^5+10x^2-19)+5x(x^3+4)lnx# 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 1307 views around the world You can reuse this answer Creative Commons License