MYTUTOR SUBJECT ANSWERS

317 views

How do I differentiate y=x^x?

y=x^x

To find the differential, dy/dx, logs of both sides must be taken:

log(y)=log(x^x)

Then using log rules, the power can be brought down, outside the log expression:

log(y) = x log(x)

This expressions can now be differentiated with respect to x, using the chain rule on the left and the product rule on the right, giving:

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

Multiplying through by y gives:

dy/dx = y (1 + log(x)) 

Remember! From the start of the question y=x^x, so this can be rewritten to:

dy/dx = x^x + x^xlog(x)

 
Pascal L. GCSE Maths tutor, A Level Maths tutor, GCSE Biology tutor, ...

2 years ago

Answered by Pascal, an A Level Maths tutor with MyTutor

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

175 SUBJECT SPECIALISTS

£20 /hr

Linden S.

Degree: Economics and Finance (Bachelors) - Exeter University

Subjects offered: Maths, Economics

Maths
Economics

“I am currently in my third year studying economics and finance at the  University of Exeter. As well as having a strong passion for economics, I have a great love for mathematics too. I have experience in teaching through coaching ten...”

£20 /hr

Jack G.

Degree: Politics, Philosophy, and Economics (Bachelors) - Warwick University

Subjects offered: Maths, Religious Studies+ 2 more

Maths
Religious Studies
Economics
.TSA. Oxford.

“Hello, I'm Jack and am studying politics, philosophy, and economics at Warwick.  Having recently been through the subjects I'm looking to tutor I feel like I know first hand what difficulties you'll be facing. I always found I wanted ...”

MyTutor guarantee

£20 /hr

Lewis M.

Degree: Biology (Masters) - Bristol University

Subjects offered: Maths, Biology

Maths
Biology

“About Me: I am a Biology student at Bristol University. I have always loved science and maths and I hope this will come across in my sessions! I have been invloved with tutoring for the majority of my school life, taking time out of ...”

MyTutor guarantee

About the author

Pascal L.

Currently unavailable: for new students

Degree: Engineering (Masters) - Durham University

Subjects offered: Maths, Science+ 3 more

Maths
Science
Physics
Chemistry
Biology

“I'm a tutor from Durham University who's ready and able to help you improve your grades!”

You may also like...

Other A Level Maths questions

Prove that the indefinite integral of I = int(exp(x).cos(x))dx is (1/2)exp(x).sin(x) + (1/2)exp(x).cos(x) + C

How do you resolve forces?

What is the chain rule and how does it work?

How do you integrate 3x^2 - 6x + 5 (wrt x)?

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok