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Differentiate y = x^x^x 2017-03-19
From Nafis:
differentiate y = x^x^x
Answered by Penny Nom.
Differentiate x^x - 2^sinx 2013-08-09
From tarun:
derivative of x^x - 2^sinx
Answered by Penny Nom.
The derivative of y=x^x 2010-04-09
From David:
So, its David, and I was wondering about the derivative of y=x^x. I have often seen it be shown as x^x(ln(x)+1), but when I did it through limits it turned out differently. Here's what I did:
It is commonly know that df(x)/dx of a function is also the limit as h->0 of f(x+h)-f(x)/h. To do this for x^x you have to start with lim h->0 ((x+h)^(x+h)-x^x)/h. The binomial theorem then shows us that this is equal to lim h->0 (x^(x+h)+(x+h)x^(x+h-1)h+...-x^x)/h
This is also equal to lim a->0 lim h->0 (x^(x+a)+(x+h)x^(x+h-1)h...-x^x)/h.
Evaluating for a=0 you get lim h->0 (x^x+(x+h)x^(x+h-1)h...x^x)/h
Seeing as the last 2 terms on the numerator cancel out you can simplify to a numerator with h's is each of the terms, which you can then divide by h to get:
lim h->0 (x+h)x^(x+h-1)... which when evaluated for h=0 gives us: x(x^(x-1)). This statement is also equal to x^x.
This contradicts the definition of the derivative of x^x that is commonly shown. So, my question is: can you find any flaws in the logic of that procedure? I do not want to be shown how to differentiate x^x implicitly because I already know how to do that.

Answered by Robert Dawson.
x^x = 1 2009-08-28
From Waleed:
Answered by Robert Dawson.
The integral of x^x 2009-06-18
what would be the integration of (X^Xdx)?

give answer in details.

Answered by Robert Dawson and Harley Weston.
Differentiate y= (x^x^x)^x 2008-06-27
From emril:
Differentiate y= (x^x^x)^x
Answered by Harley Weston.
differentiate Y=X^X^X 2004-09-13
From Kunle:
differentiate Y=X^X^X
Answered by Penny Nom.
The derivative of x to the x 2004-02-14
From Cher:
what about the derivative of x to the power x?
Answered by Penny Nom.
Integrating x^x 2002-06-18
From Jeremy:
I am a student at the University of Kansas and I am wondering if there is a general anti-derivative for x x (i.e. the integral of x x dx)? I've looked in a bunch of Table of Integrals and have found nothing (can you guys find it?), so I'm sort of wondering if this may be a research type question.
Answered by Claude Tardif.



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