How do you differentiate x^x?

To differentiate xx, we first let y = xx. (Note that xx is not in the form xc where c is a constant or ax where a is a constant so the usual differentiation formulas cannot be used). The trick here is to take the natutral logarithm of both sides. Then you obtain, ln(y) = ln(xx). From here you need to use the rule that ln(xx) = xln(x). So currently we have ln(y) = xln(x). From here we can differentiate implicitly to get: 1/y multiplied by dy/dx = ln(x) + 1 (differentiate right hand side using product rule and left hand side using chain rule).The final step is to multiply through by y and substitute xx back in for y. This gives you: dy/dx = xx(ln(x) + 1).  

AP
Answered by Anish P. Maths tutor

3118 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

solve 2cos^2(x) - cos(x) = 0 on the interval 0<=x < 180


What does dy/dx represent?


Differentiate x^3⋅cos(5⋅x) with respect to x.


f(x) = 2 / (x^2 + 2). Find g, the inverse of f.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning