Find the derivative of the function f:(0,oo)->R, f(x)=x^x.

The domain of the function allows us to write f(x)=xx  as f(x)=eln(x^x)=ex ln(x) (since ln(x) is defined on (0,oo) only). Using the standard derivative rules we get f'(x)=ex ln(x) (x ln(x))'=ex ln(x)(1+ln(x))=xx (1+ln(x)).

AR
Answered by Andrei R. Maths tutor

2875 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate 3t^2 + 7t with respect to t, between 1 and three.


Find the set of values for which x^2 - 7x - 18 >0


f(x)=x^3 + x^2 -10x +8 show that (x-1) is a factor of f(x), Factorise f(x) fully , sketch the graph of f(x)


what is implicit differentiation and how is it achieved?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences