Find the derivative of x^x

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / Find the derivative of x^x

649 views

Find the derivative of x^x

y = x^x -- Yikes! Doesn't that look ugly.
It's mostly the x^x part, since ... to the x is fine, and x to the ... is fine.
We must split the two x's in order to continue.
Perhaps we could log? since then we can pull the index to the front.
so: log(y) = log(x^x) = x log(x) -- because [log(a^b) = b log(a)]
Well this looks much better. On the left we have something which is easy using chain rule
and the right side, looks easy using product rule.

So:
d/dx log(y) = dy/dx * (1/y)
and:
d/dx x*log(x) = 1*log(x) + x*(1/x)
= log(x) + 1

so:
dy/dx * (1/y) = 1 + log(x)
Multiplying through by y, gives us:
dy/dx = y ( 1 + log(x) )
but remember, y = x^x
so dy/dx = x^x ( 1 + log(x) )

Mayur D. A Level Maths tutor, A Level Further Mathematics tutor, GCS...

2 years ago

Answered by Mayur, an A Level Maths tutor with MyTutor

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

354 SUBJECT SPECIALISTS

£26 /hr

George B.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

“Premium tutor. First class graduate with teaching experience from a top Russell Group university. I deliver fun and relaxed lessons which achieve results!”

5.0

26 reviews | 92 completed tutorials

Save profile

Ruth N. GCSE Economics tutor, A Level Economics tutor, IB Economics t...

View profile

£20 /hr

Ruth N.

Degree: Economics (Bachelors) - Cambridge University

Subjects offered:Maths, Economics+ 2 more

“Economics Graduate from Cambridge, wanting to share my passion for the discipline”

5.0

3 reviews | 5 completed tutorials

Save profile

Mabast H. GCSE Physics tutor, A Level Physics tutor, IB Physics tutor...

View profile

£20 /hr

Mabast H.

Degree: Physics (Bachelors) - Imperial College London University

Subjects offered:Maths, Physics+ 3 more

“Undergraduate Physicist with lots of experience in teaching in different fields and age groups, looking to instil a passion for learning into students.”

4.0

3 reviews | 4 completed tutorials

Save profile

See more A Level Maths tutors

About the author

View profile

Mayur D.

Currently unavailable: until 30/06/2017

Degree: MMath ( G103) (Masters) - Warwick University

Subjects offered:Maths, Physics+ 2 more

“I am a cheerful experienced tutor, having taught both in classrooms and one-on-one. Doing so has taught me a range of teaching techniques such that if one doesn't work for you, you can rest assured I have one that will help. ”

4.9

21 reviews | 102 completed tutorials

Save profile

Version:	3.49.1
Build:	7666049797d9
Time:	2017-08-13T14:18:20Z

MYTUTOR SUBJECT ANSWERS

Find the derivative of x^x

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

354 SUBJECT SPECIALISTS

About the author

You may also like...

Other A Level Maths questions

One-to-one help is at your fingertips