Differentiate x^x

With the methods we know at A Level we cannot current differentiate xx in its current form. Therefore let y = xxTo turn it into a form we can differentiate we take the natural log of both sides. This gives ln(y) = ln(xx). Using the log rule (logab = bloga) we can then say ln(y) = xln(x). We can then differentiate implicitly to form a differential equation 1/y x dy/dx = ln(x) + 1. To find dy/dx we then simply multiply through by y to give...dy/dx = y(lnx + 1) = xx(lnx + 1)

Answered by Maths tutor

2736 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I integrate cos^2(x)?


Find the exact value of the integral of (2+7/x), between x=1 and x=e. Give your answer in terms of e.


Integrate the expression cos^2(x).


Given (x-2) is a factor of ax^3 + ax^2 + ax - 42, find the value of a


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