MYTUTOR SUBJECT ANSWERS

400 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

180 SUBJECT SPECIALISTS

£24 /hr

Shruti V.

Degree: Biomedical Engineering (Masters) - Southampton University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Chemistry
-Personal Statements-

“Who Am I? I am a Masters Biomedical Engineering student at the University of Southampton, having already completed a degree in Aerospace Engineering achieving a First Class (Honours). I have a real passion and love for science and ma...”

£20 /hr

Shaun F.

Degree: Mathematics with International Study (Masters) - Exeter University

Subjects offered: Maths

Maths

“Hi, I'm Shaun! I'm currently studying for a masters in Mathematics at the University of Exeter..”

MyTutor guarantee

£24 /hr

Nathan L.

Degree: Materials Science (Masters) - Oxford, St Edmund Hall University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Chemistry

“About Me: I'm a first year Materials science undergraduate at The University of Oxford. I loved learning about science and maths at school and hope my tutorials make you feel the same.  Structure: The key concept about tutorials i...”

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

Polynomial long division, how do I do it?

For the curve f(x) = 2x^3 - 54x, find the stationary points and state the nature of these points

Differentiate ln(x)/x

How do I use the product rule for differentiation?

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