Differentiate #y=x^x#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Shwetank Mauria Mar 27, 2016 #(dy)/(dx)=(1+lnx)x^x# Explanation: As #y=x^x#, we have #lny=lnx^x=xlnx# Hence differentiating both sides, #1/yxx(dy)/(dx)=1xxlnx+x xx1/x# or #1/(x^x)xx(dy)/(dx)=1+lnx# and hence #(dy)/(dx)=(1+lnx)x^x# Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of #y= 6cos(x^2)# ? How do you find the derivative of #y=6 cos(x^3+3)# ? How do you find the derivative of #y=e^(x^2)# ? How do you find the derivative of #y=ln(sin(x))# ? How do you find the derivative of #y=ln(e^x+3)# ? How do you find the derivative of #y=tan(5x)# ? How do you find the derivative of #y= (4x-x^2)^10# ? How do you find the derivative of #y= (x^2+3x+5)^(1/4)# ? How do you find the derivative of #y= ((1+x)/(1-x))^3# ? See all questions in Chain Rule Impact of this question 1087 views around the world You can reuse this answer Creative Commons License