How do you find the derivative of #y = x^(ln x)#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Jim H Aug 9, 2016 Rewrite as: #y = e^ln(x^lnx) = e^(lnxlnx) = e^((lnx)^2)# Explanation: Now differentiate using the chain rule #dy/dx = e^((lnx)^2)[2(lnx)(1/x)]# # = (2lnx)/x x^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 11134 views around the world You can reuse this answer Creative Commons License