How do you find the derivative of #f(x) = x^2 * ln(x) #? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Andrea S. Dec 22, 2016 #d/(dx) (x^2lnx) = x(1+2lnx)# Explanation: You can differentiate #f(x)# using the product rule: #d/(dx) (x^2lnx) = d/(dx) x^2* lnx + x^2 d/(dx) lnx = 2xlnx +x^2*1/x= 2xlnx+x=x(1+2lnx)# 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 1729 views around the world You can reuse this answer Creative Commons License