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differentiation using product rule

x^x (1+ln x)

differentiated

when i do it i miss out a (1 + ln x)

can someone go through it please?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: differentiation using product rule

Use another pair of parenthesis please to make it clearer what the problem is.
Like is it?
#1.)  (x^x)(1+ln x)
or
#2.) x^(x(1 + ln x))
Which one is it?

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Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: differentiation using product rule

Use another pair of parenthesis please to make it clearer what the problem is.
Like is it?
#1.)  (x^x)(1+ln x)
or
#2.) x^(x(1 + ln x))
Which one is it?

I think it's more likely to be #1.

Differentiating

seperately first gives:

Using this result, and the product rule, to differentiate the whole expression:

Last edited by Daniel123 (2008-06-11 22:02:38)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: differentiation using product rule

Actually, I spotted a nicer way to differentiate

Rewriting as: