. centre de ressources dilemmes et doutes le visage humain de mathématiques Qui sommes-nous Problème de mois activités de promotion babillard
Centrale des maths - centraledesmaths.uregina.ca
Dilemmes & doutes
« D & D »
. .
topic card  



liste de
. .
nouvelle recherche

9 articles trouvés pour ce sujet.
Differentiate y = x^x^x 2017-03-19
Nafis pose la question :
differentiate y = x^x^x
Penny Nom lui répond.
Differentiate x^x - 2^sinx 2013-08-09
tarun pose la question :
derivative of x^x - 2^sinx
Penny Nom lui répond.
The derivative of y=x^x 2010-04-09
David pose la question :
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.

Robert Dawson lui répond.
x^x = 1 2009-08-28
Waleed pose la question :
Robert Dawson lui répond.
The integral of x^x 2009-06-18
ANGIKAR pose la question :
what would be the integration of (X^Xdx)?

give answer in details.

Robert Dawson and Harley Weston lui répond.
Differentiate y= (x^x^x)^x 2008-06-27
emril pose la question :
Differentiate y= (x^x^x)^x
Harley Weston lui répond.
differentiate Y=X^X^X 2004-09-13
Kunle pose la question :
differentiate Y=X^X^X
Penny Nom lui répond.
The derivative of x to the x 2004-02-14
Cher pose la question :
what about the derivative of x to the power x?
Penny Nom lui répond.
Integrating x^x 2002-06-18
Jeremy pose la question :
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.
Claude Tardif lui répond.



Centrale des maths reçoit une aide financière de l’Université de Regina et de The Pacific Institute for the Mathematical Sciences.



accueil centre de ressources accueil Société mathématique du Canada l'Université de Regina PIMS