  Math Central - mathcentral.uregina.ca  Quandaries & Queries    Q & Q    Topic: x^x   start over

9 items are filed under this topic.    Page1/1            Differentiate y = x^x^x 2017-03-19 From Nafis:differentiate y = x^x^xAnswered by Penny Nom.     Differentiate x^x - 2^sinx 2013-08-09 From tarun:derivative of x^x - 2^sinxAnswered 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:x^x=1Answered by Robert Dawson.     The integral of x^x 2009-06-18 From ANGIKAR: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)^xAnswered by Harley Weston.     differentiate Y=X^X^X 2004-09-13 From Kunle:differentiate Y=X^X^XAnswered 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.      Page1/1    Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.    about math central :: site map :: links :: notre site français