What is the derivative of x^x

  • Google+ icon
  • LinkedIn icon
  • 795 views

Firstly we should notice the similarities between this expression and expressions of the standard type ax. 

To deal with this type of expression, we take logarithms of both sides and then apply the usual rules of differentiation. Let's try that here:

1.) y = x 

take logs of both sides and use the multiplicative law of logarithms 

2.) log(y) = x*log(x)

now use the chain rule on the LHS and the product rule on the RHS

3.) dy/dx * 1/y = 1 + log(x)

now simply rearrange to find dy/dx

4.) dy/dx = x*log(x)*(1+log(x))

Daniel K. GCSE Maths tutor, A Level Maths tutor, A Level Physics tuto...

About the author

is an online A Level Maths tutor with MyTutor studying at Oxford, Merton College University

Still stuck? Get one-to-one help from a personally interviewed subject specialist.

95% of our customers rate us

Browse tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok